% File name: ad2000.bib % Title: Bibliography of Automatic Differentiation % Compiled by: George F. Corliss, Marquette University, Milwaukee % % BibTex source file for % George Corliss, Christ{\`e}le Faure, Andreas Griewank, % Laurent Hasco{\"e}t, and Uwe Naumann (eds.), % Automatic Differentiation: From Simulation to Optimization, % Springer, New York, 2001. % \begin {abstract} % This is a bibliography of work related to automatic % differentiation. It represents the compilation of all works cited % by all chapters in this volume, {\sl Automatic Differentiation: From % Simulation to Optimization,} George Corliss, Christ{\`e}le % Faure, Andreas Griewank, Laurent Hasco{\"e}t, and Uwe Naumann % (eds.), Springer, New York, 2001~\cite{Corliss2001b}. Authors % compiled bibliographies for their own chapters. The separate % bibliographies were merged into a single BibTex database. Because % it includes all of the works cited by any chapter in this book, it % includes most widely cited AD work and many citations that are % not directly related to AD. For example, it includes basic % references in optimization, symbolic algebra systems, and several % applications areas. % \end {abstract} \Sort{ Mode{on} Collation{mixed} SortTypeOrder{key,name} NameOrder{ascending} Key{key} KeyOrder{ascending,nulls first} } @INPROCEEDINGS{Abate1997a, author = "Jason Abate and Christian Bischof and Alan Carle and Lucas Roh", editor = "", year = 1997, title = "Algorithms and Design for a Second-Order Automatic Differentiation Module", booktitle = "International Symposium on Symbolic and Algebraic Computing (ISSAC)", series = "", number = "", pages = "149--155", note = "", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Abate1997a", abstract = "", comment = "", keywords = "", referred = "[Mor\'e2001a]." } @INCOLLECTION{Abate2001a, author = "Jason Abate and Steve Benson and Lisa Grignon and Paul D.~Hovland and Lois C. McInnes and Boyana Norris", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Integrating {AD} with Object-Oriented Toolkits for High-performance Scientific Computing", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 20, pages = "173--178", note = "", publisher = "Springer", address = "New York", key = "Abate2001a", crossref = "Corliss2001b", abstract = "Often the most robust and efficient algorithms for the solution of large-scale problems involving nonlinear PDEs and optimization require the computation of derivatives. We examine the use of automatic differentiation (AD) for computing first and second derivatives in conjunction with two parallel toolkits, the Portable, Extensible Toolkit for Scientific Computing (PETSc) and the Toolkit for Advanced Optimization (TAO). We discuss how the use of mathematical abstractions in PETSc and TAO facilitates the use of AD to automatically generate derivative codes and present performance data demonstrating the suitability of this approach.", comment = "Mathematics and Computer Science Division, Argonne National Laboratory preprint ANL/MCS-P820-0500", keywords = "", referred = "[Lee2001a], [Mor\'e2001a].", isbn = "" } @TECHREPORT{Abbott1991a, author = "John Abbott and Andr{\'e} Galligo", month = "", year = 1991, title = "Reversing a Finite Sequence", number = "", address = "", institution = "", key = "Abbott1991a", type = "Preprint", abstract = "", comment = "", keywords = "", referred = "[Grimm1996a]." } @INBOOK{Abragam1972a, author = "Anatole Abragam and Berbis Bleaney", editor = "", year = 1972, title = "R{\'e}sonance paramagn{\'e}tique {\'e}lectronique des ions de transition", booktitle = "", series = "", number = "", chapter = "3.2. L'effet de l'anisotropie sur le facteur g, formule (3,10)", pages = "", note = "", publisher = "Presses {U}niversitaires de {F}rance, Paris", address = "", key = "Abragam1972a", abstract = "", comment = "", keywords = "", referred = "[Souli\'e2001a]." } @BOOK{Abramowitz1964a, editor = "Milton Abramowitz and Irene A. Stegun", year = 1964, title = "Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables", series = "", number = "", note = "", publisher = "U.S. Government Printing Office", address = "Washington, D.C., 20402", key = "Abramowitz1964a", abstract = "", comment = "", keywords = "", referred = "[Flanders2001a], [Souli\'e2001a]." } @BOOK{Aho1995a, author = "Alfred V. Aho and Ravi Sethi and Jeffrey D. Ullman", year = 1995, title = "Compilers: Principles, Techniques, and Tools", series = "", number = "", note = "", publisher = "Addison-Wesley", address = "Reading, Mass.", key = "Aho1995a", abstract = "", comment = "", keywords = "", referred = "", isbn = 0201100886 } @ARTICLE{Albou2000a, author = "A. F. Albou and V. I. Gorbunov and V. I. Zubov", month = "", year = 2000, title = "Optimal Control of the Process of Melting", journal = "Computational Mathematics and Mathematical Physics", volume = 40, number = 4, pages = "491--504", note = "", key = "Albou2000a", abstract = "", comment = "", keywords = "", referred = "[Evtushenko2001a]." } @BOOK{Alefeld1983a, author = "G{\"o}tz Alefeld and J{\"u}rgen Herzberger", year = 1983, title = "Introduction to Interval Computations", series = "", publisher = "Academic Press", address = "New York", key = "Alefeld1983a", abstract = "", comment = "", keywords = "", referred = "[Berz2001a], [Irim1991a], [Makino2001a].", isbn = "0--12--049820--0" } @MASTERSTHESIS{Allen1997a, author = "J.~Allen", month = "", year = 1997, title = "Computer Optimisation of Cornering Line", note = "See \url{www.cranfield.ac.uk/cils/library}.", address = "", school = "School of Mechanical Engineering, Cranfield University", key = "Allen1997a", abstract = "", comment = "", keywords = "", referred = "[Casanova2001a]." } @INPROCEEDINGS{Altpeter2000a, author = "R.~Altpeter and Wolfram Klein", editor = "", year = 2000, title = "Numerical Solutions in Stationary Thermodynamic Calculations of Steam Generators", booktitle = "Proceedings of GAMM 2000", pages = "", publisher = "", address = "", key = "Altpeter2000a", abstract = "", comment = "", keywords = "", referred = "[Klein2001a]." } @MISC{AMPL2000a, author = "", month = "", year = "", title = "{AMPL}", note = "See \url{www.ampl.com}", howpublished = "", key = "AMPL2000a", abstract = "", comment = "", keywords = "", referred = "[Mor\'e2001a]." } @BOOK{Anderson1995a, author = "E. Anderson and Z. Bai and Christian Bischof and John Demmel and Jack Dongarra and J. {Du Croz} and A. Greenbaum and Sven Hammarling and A. McKenney and S. Ostrouchov and Danny Sorensen", editor = "", year = 1995, title = "LAPACK User's Guide, 2nd edn.", series = "", number = "", note = "", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Anderson1995a", abstract = "", comment = "", keywords = "", referred = "[Cappelaere2001a].", isbn = "0-89871-345-5" } @ARTICLE{Anderson1999a, author = "W. Kyle Anderson and Daryl L. Bonhaus", month = "", year = 1999, title = "Airfoil Design on Unstructured Grids for Turbulent Flows", journal = "AIAA J.", volume = 37, number = 2, pages = "185--191", note = "", key = "Anderson1999a", abstract = "", comment = "", keywords = "", referred = "[Giles2001a]." } @INPROCEEDINGS{Anderson1999b, author = "W. Kyle Anderson and William D. Gropp and Dinesh K. Kaushik and David E. Keyes and Barry F. Smith", editor = "", year = 1999, title = "Achieving High Sustained Performance in an Unstructured Mesh {CFD} Application", booktitle = "Proceedings of SC'99", series = "", number = "", pages = "", note = "{G}ordon {B}ell {P}rize {A}ward Paper in the ``{S}pecial'' {C}ategory", publisher = "IEEE Computer Society", address = "", key = "Anderson1999b", abstract = "", comment = "", keywords = "", referred = "[Keyes2001a]." } @ARTICLE{Arbetter1999a, author = "T.~E.~Arbetter and J.~A.~Curry and J.~A.~Maslank", month = "", year = 1999, title = "Effects of Rheology and Ice Thickness Distribution in a Dynamic-Thermodynamic Sea-Ice Model", journal = "J.~Phys.~Oceanog.", volume = 29, number = "", pages = "2656--2670", note = "", key = "Arbetter1999a", abstract = "", comment = "", keywords = "", referred = "[Abate2001a]." } @BOOK{Ascher1988a, author = "Uri M. Ascher and Robert M. Mattheij and Robert D. Russell", year = 1988, title = "Numerical Solution of Boundary Value Problems", series = "", number = "", publisher = "Prentice Hall", address = "Englewood Cliffs, N.J.", key = "Ascher1998a", abstract = "", comment = "", keywords = "", referred = "[Caillau2001a], [Guckenheimer1996a].", isbn = "" } @ARTICLE{Aubert1996a, author = "Pierre Aubert and Bernard Rousselet", month = "", year = 1998, title = "Sensitivity Computations and Shape Optimization for a Nonlinear Arch Model with Simple Instabilities", journal = "IJNME", volume = 42, number = "", pages = "15--48", note = "", key = "Aubert1996a", abstract = "", comment = "", keywords = "", referred = "[Aubert2001a]." } @ARTICLE{Aubert2000a, author = "Pierre Aubert and Nicolas {Di~C{\'e}sar{\'e}} and Olivier Pironneau", month = "", year = 2000, title = "Automatic Differentiation in {C++} using Expression Templates and Application to a Flow Control Problem", journal = "Computing and Visualisation in Sciences", volume = "", number = "", pages = "", note = "Accepted. See \url{pierre.aubert.free.fr/research/fad.ps}", key = "Aubert2000a", abstract = "", comment = "", keywords = "", referred = "[Aubert2001a]." } @ARTICLE{Aubert2000b, author = "Pierre Aubert", month = "", year = 2000, title = "meta::{E}xpr$\langle${T}\_emplate$\rangle$ A Library for Building Efficient Numerical Analysis Classes in {C++}", journal = "Journal of Computational and Applied Mathematics", volume = "", number = "", pages = "", note = "Submitted. See \url{pierre.aubert.free.fr/research/meta.ps}", key = "Aubert2000b", abstract = "", comment = "", keywords = "", referred = "[Aubert2001a]." } @INCOLLECTION{Aubert2001a, author = "Pierre Aubert and Nicolas {Di~C{\'e}sar{\'e}}", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Expression Templates and Forward Mode Automatic Differentiation", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 37, pages = "311--315", note = "", publisher = "Springer", address = "New York", key = "Aubert2001a", crossref = "Corliss2001b", abstract = "This work deals with an implementation of automatic differentiation of \cpp{} computer programs in forward mode using operator overloading and expression templates. In conjunction with a careful reuse of data, this technique also improves performance of programs involving linear algebra computations mixed or not with automatic differentiation. We give a broad view of implementation and explain some important concepts regarding code optimization. We conclude with some benchmarks applied to our optimal control software.", comment = "", keywords = "", referred = "", isbn = "" } @TECHREPORT{Averick1991a, author = "Brett M. Averick and Jorge J. Mor{\'e}", month = "", year = 1991, title = "User Guide for the {MINPACK-2} Test Problem Collection", number = "ANL/MCS-TM-157", note = "Also issued as Preprint 91-101 of the Army High Performance Computing Research Center at the University of Minnesota.", address = "Argonne, Ill.", institution = "Argonne National Laboratory", key = "Averick1991a", type = "Technical Memorandum", abstract = "", comment = "", keywords = "", referred = "[Mor\'e2001a]." } @TECHREPORT{Averick1992a, author = "Brett M.~Averick and Richard G.~Carter and Jorge J.~Mor{\'e} and Guo-Liang Xue", month = "", year = 1992, title = "The {MINPACK-2} Test Problem Collection", number = "MCS--P153--0692, ANL/MCS--TM--150, Rev. 1", note = "See \url{ftp://info.mcs.anl.gov/pub/MINPACK-2/tprobs/P153.ps.Z}", address = "Argonne, Ill.", institution = "Mathematics and Computer Science Division, Argonne National Laboratory", key = "Averick1992a", type = "Preprint", abstract = "", comment = "", keywords = "", referred = "[Abate2001a], [Bischof1996b], [Gay1996a], [Geitner1996a], [Mancini2001a]." } @ARTICLE{Averick1994a, author = "Brett M. Averick and Jorge J. Mor{\'e} and Christian H. Bischof and Alan Carle and Andreas Griewank", month = "", year = 1994, title = "Computing Large Sparse {J}acobian Matrices Using Automatic Differentiation", journal = "SIAM J. Sci. Comput.", volume = 15, number = 2, pages = "285--294", key = "Averick1994a", abstract = "", comment = "Also appeared as Preprint MCS-P348-0193.", keywords = "", referred = "[Hossain2001a], [Bischof1996a], [Coleman1996a], [Griewank2001a]." } @ARTICLE{Bacon1994a, author = "David F. Bacon and Susan L. Graham and Oliver J. Sharp", month = "", year = 1994, title = "Compiler Transformations for High-Performance Computing", journal = "ACM Computing Surveys", volume = 26, number = 4, pages = "345--420", note = "", key = "Bacon1994a", abstract = "", comment = "", keywords = "", referred = "[Bodin2001a]." } @INPROCEEDINGS{Balay1997a, author = "Satish Balay and William D.~Gropp and Lois C. McInnes and Barry F.~Smith", editor = "E.~Arge and A.~M.~Bruaset and Hans Petter Langtangen", year = 1997, title = "Efficient Management of Parallelism in Object Oriented Numerical Software Libraries", booktitle = "Modern Software Tools in Scientific Computing", pages = "163--202", publisher = "Birkhauser Press", key = "Balay1997a", referred = "[Abate2001a]." } @TECHREPORT{Balay2000a, author = "Satish Balay and William D.~Gropp and Lois C. McInnes and Barry F.~Smith", month = "Mar.", year = 2000, title = "The Portable Extensible Toolkit for Scientific Computing {PETS}c 2.0 Users Manual", number = "ANL-95/11 - Revision 2.0.28", note = "See \url{www.mcs.anl.gov/petsc}", address = "", institution = "Argonne National Laboratory", key = "Balay2000a", type = "", abstract = "", comment = "", keywords = "", referred = "[Abate2001a], [Keyes2001a]." } @INBOOK{Ball1969a, author = "William E. Ball", year = 1969, title = "Material and Energy Balance Computations", booktitle = "", series = "", number = "", pages = "560--566", note = "", publisher = "John Wiley", address = "", key = "Ball1969a", abstract = "", comment = "", keywords = "", referred = "[Souli\'e2001a]." } @TECHREPORT{Baratchart1998a, author = "L. Baratchart and Jos{\'e} Grimm and J. Leblond and M. Olivi and F. Seyfert and F. Wielonsky", month = "", year = 1998, title = "Identification d'un filtre hyperfr\'equences par approximation dans le domaine complexe", number = "RT-0219", note = "", address = "", institution = "INRIA", key = "Baratchart1998a", type = "", abstract = "", comment = "", keywords = "", referred = "[Grimm2001a]." } @ARTICLE{Bartholomew-Biggs1998a, author = "Michael C.~Bartholomew-Biggs", month = "", year = 1998, title = "Using Forward Accumulation for Automatic Differentiation of Implicitly-Defined Functions", journal = "Computational Optimization and Applications", volume = 9, number = "", pages = "65--84", note = "", key = "Bartholomew-Biggs1998a", abstract = "Uses post-differentiation to differentiate implictly defined function. Notes that full differentiation - i.e. AD throughout an iterative solver generates worse results than post-differentiation.", comment = "", keywords = "", referred = "[Forth2001a], [Lee2001a]." } @ARTICLE{Bartholomew-Biggs2000a, author = "Michael C.~Bartholomew-Biggs", month = "", year = 2000, title = "A Two-dimensional Search used with a Non-linear Least-squares Solver", journal = "Journal of Optimization Theory and Applications", volume = 104, number = 1, pages = "215--234", note = "", key = "Bartholomew-Biggs2000a", abstract = "", comment = "", keywords = "", referred = "[Christianson2001a]." } @ARTICLE{Bartholomew-Biggs2000b, author = "Michael C.~Bartholomew-Biggs and Steve Brown and Bruce Christianson and Laurence C. W. Dixon", month = "", year = 2000, title = "Automatic Differentiation of Algorithms", journal = "Journal of Computational and Applied Mathematics", volume = 124, number = "", pages = "171--190", note = "", key = "Bartholomew-Biggs2000b", abstract = "", comment = "", keywords = "", referred = "[Christianson2001a]." } @BOOK{Barton1994a, author = "John J. Barton and Lee R. Nackman", editor = "", year = 1994, title = "Scientific and Engineering {C++}", series = "", number = "", note = "", publisher = "Addison-Wesley", address = "Reading, Mass.", key = "Barton1994a", abstract = "This book's three parts take readers with no prior C++ knowledge all the way from basic concepts, through object-oriented programming and design techniques, to advanced C++ features and techniques. Coverage of object-oriented programming emphasizes various methods of expressing commonality and abstraction, and the advanced coverage illustrates coordination of advanced C++ by developing several interesting examples. (From Amazon.com)", comment = "", keywords = "", referred = "[Aubert2001a].", isbn = 0201533936 } @ARTICLE{Bates1980a, author = "Douglas M. Bates and Donald G. Watts", month = "", year = 1980, title = "Relative Curvature Measures of Nonlinearity", journal = "Journal of the Royal Statistical Society B", volume = 42, number = 1, pages = "1--25", note = "", key = "Bates1980a", abstract = "", comment = "", keywords = "", referred = "[Huiskes2001a]." } @INCOLLECTION{Battermann1998a, author = "A. Battermann and M. Heinkenschloss", editor = "W. Desch and F. Kappel and K. Kunisch", year = 1998, title = "Preconditioners for {K}arush-{K}uhn-{T}ucker Matrices Arising in Optimal Control of Distributed Systems", booktitle = "Optimal Control of Partial Differential Equations (Vorau 1996)", series = "", number = "", pages = "15--32", note = "", publisher = "Birkheuser Verlag", address = "Basel", key = "Battermann1998a", abstract = "", comment = "Also appeared as TR96--34, Department of Computational and Applied Mathematics, Rice University.", keywords = "", referred = "[Keyes2001a].", isbn = "" } @ARTICLE{Bauer1974a, author = "Friedrich L. Bauer", month = "", year = 1974, title = "Computational Graphs and Rounding Errors", journal = "SIAM J. Numer. Anal.", volume = 11, number = 1, pages = "87--96", note = "", key = "Bauer1974a", abstract = "", comment = "", keywords = "", referred = "[Braconnier2001a]." } @ARTICLE{Beck1995a, author = "T. Beck and Herbert Fischer", month = "", year = 1995, title = "The {IF}-Problem in Automatic Differentiation", journal = "Journal of Comput. Appl. Math.", volume = 50, number = "", pages = "119--131", key = "Beck1995a", abstract = "", comment = "", keywords = "", referred = "[Berz2001a], [Kearfott1996a]." } @INCOLLECTION{Beley2001a, author = "Jean-Daniel Beley and Stephane Garreau and Frederic Thevenon and Mohamed Masmoudi", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Application of Higher Order Derivatives to Parameterization", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 40, pages = "335--341", note = "", publisher = "Springer", address = "New York", key = "Beley2001a", crossref = "Corliss2001b", abstract = "Research on automatic differentiation is mainly motivated by gradient computation and optimization. However, in the optimal design area, it is quite difficult to use optimization tools. Some constraints (e.g. aesthetics constraints, manufacturing constraints) are quite difficult to describe by mathematical expressions. In practice, the optimal design process is a dialog between the designer and the analysis software (structural analysis, electromagnetism, computational fluid dynamics, etc.). One analysis may take a while. Hence, parameterization tools such as design of experiments (D.O.E.) and neural networks are used. The aim of those tools is to build surrogate models. We present a parameterization method based on higher order derivatives computation obtained by automatic differentiation.", comment = "", keywords = "", referred = "", isbn = "" } @INCOLLECTION{Ben-Haj-Yedder2001a, author = "Adel {Ben-Haj-Yedder} and Eric Cances and Claude {Le Bris}", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Optimal Laser Control of Chemical Reactions Using {AD}", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 24, pages = "205--211", note = "", publisher = "Springer", address = "New York", key = "Ben-Haj-Yedder2001a", crossref = "Corliss2001b", abstract = "This paper presents an application of automatic differentiation to a control problem from computational quantum chemistry. The goal is to {\bf control the orientation of a linear molecule} by using a designed laser pulse. In order to optimize the shape of the pulse we experiment with a nonlinear conjugate gradient algorithm as well as various stochastic procedures. Work in progress on robust control is also mentioned.", comment = "", keywords = "", referred = "[Faure2001a].", isbn = "" } @INCOLLECTION{Benary1996a, author = "Jochen Benary", editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank", year = 1996, title = "Parallelism in the Reverse Mode", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "137--147", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Benary1996a", crossref = "Berz1996c", abstract = "In the basic form of the reverse mode for calculating derivatives, the amount of memory needed to record the intermediate values can become excessively large for problems of practical interest. If sequential checkpointing schemes are used, the memory requirement can be dramatically reduced, but the run time may be significantly increased. Implementing suitable checkpointing schemes on multiprocessor systems can decrease the run time to its theoretical minimum. Among the many possible scheduling strategies, we develop one that minimizes resource requirements. We present different communication structures that depend on the memory architecture of the multiprocessor system and the available resources. We also estimate the limits of the complexity and the memory requirements of the problem function.", comment = "", keywords = "Parallelism, reverse mode, checkpointing, snapshots.", referred = "[Mancini2001a]." } @BOOK{Bendsoe1995a, author = "Martin P. Bends{\o}e", editor = "", year = 1995, title = "Optimization of Structural Topology, Shape and Material", series = "", number = "", note = "", publisher = "Springer", address = "Berlin", key = "Bendsoe1995a", abstract = "", comment = "", keywords = "", referred = "[Haase2001a].", isbn = "" } @TECHREPORT{Bendtsen1996a, author = "Claus Bendtsen and Ole Stauning", month = "", year = 1996, title = "{FADBAD}, a Flexible {C++} Package for Automatic Differentiation", number = "IMM-REP-1996-17", note = "", address = "Lyngby", institution = "Technical University of Denmark, IMM, Departement of Mathematical Modeling", key = "Bendtsen1996a", type = "{T}echnical {R}eport", abstract = "", comment = "", keywords = "", referred = "[Aubert2001a], [Klein2001a]." } @TECHREPORT{Benson1999a, author = "Steve Benson and Lois C. McInnes and Jorge J.~Mor{\'e}", month = "", year = 1999, title = "{GPCG}: A Case Study in the Performance and Scalability of Optimization Algorithms", number = "ANL/MCS-P768-0799", note = "", address = "", institution = "Mathematics and Computer Science Division, Argonne National Laboratory", key = "Benson1999a", type = "", abstract = "", comment = "", keywords = "", referred = "[Abate2001a]." } @TECHREPORT{Benson2000a, author = "Steve Benson and Lois C. McInnes and Jorge J. Mor{\'e}", month = "", year = 2000, title = "{TAO} Users Manual", number = "ANL/MCS-TM-242", note = "See \url{www.mcs.anl.gov/tao}", address = "", institution = "Mathematics and Computer Science Division, Argonne National Laboratory", key = "Benson2000a", type = "", abstract = "", comment = "", keywords = "", referred = "[Abate2001a]." } @BOOK{Berge1976a, author = "Claude Berge", editor = "", year = 1976, title = "Graphs and Hypergraphs", series = "", number = "", note = "", publisher = "North Holland", address = "Amsterdam", key = "Berge1976a", abstract = "", comment = "", keywords = "", referred = "[Naumann2001a].", isbn = "" } @INPROCEEDINGS{Berner1996a, author = "Sonja Berner", editor = "G{\"o}tz Alefeld and Andreas Frommer and Bruno Lang", year = 1996, title = "A Parallel Method for Verified Global Optimization", booktitle = "Scientific Computing and Validated Numerics", series = "Mathematical Research", number = "", pages = "200--206", note = "", publisher = "Akademie Verlag", address = "Berlin", key = "Berner1996a", abstract = "", comment = "", keywords = "", referred = "[Kearfott2001a]." } @BOOK{Bertsekas1991a, author = "Dimitri P. Bertsekas", editor = "", year = 1991, title = "Linear Network Optimization", series = "", number = "", note = "", publisher = "MIT Press", address = "Massachusetts and London", key = "Bertsekas1991a", abstract = "", comment = "", keywords = "", referred = "[Hoefkens2001a].", isbn = 0262023342 } @ARTICLE{Berz1989a, author = "Martin Berz", year = 1989, title = "Differential Algebraic Description of Beam Dynamics to Very High Orders", journal = "Particle Accelerators", volume = 24, number = "", pages = 109, key = "Berz1989a", abstract = "", comment = "", keywords = "", referred = "[Berz91a], [Berz1996b], [Fuchi1996a], [Hoefkens2001a], [Juedes1991a], [Klein2001a], [Pusch1996a], [Shamseddine1996a]." } @INCOLLECTION{Berz1991a, author = "Martin Berz", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "Forward Algorithms for High Orders and Many Variables with Application to Beam Physics", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "147--156", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Berz1991a", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "[Berz2001a], [Flanders1991a], [Fuchi1996a], [Kearfott2001a], [Klein2001a], [Makino2001a], [Pusch1996a].", isbn = "0--89871--284--X" } @INPROCEEDINGS{Berz1991b, author = "Martin Berz", editor = "", year = 1991, title = "Symplectic Tracking in Circular Accelerators with High Order Maps", booktitle = "Nonlinear Problems in Future Particle Accelerators", series = "", number = "", pages = 288, note = "", publisher = "World Scientific", address = "", key = "Berz1991b", abstract = "", comment = "", keywords = "", referred = "[Hoefkens2001a]." } @ARTICLE{Berz1994c, author = "Martin Berz and Georg H. Hoffst{\"a}tter", year = 1994, title = "Exact Estimates of the Long Term Stability of Weakly Nonlinear Systems Applied to the Design of Large Storage Rings", journal = "Interval Computations", volume = 2, number = "", pages = "68--89", key = "Berz1994c", abstract = "", comment = "", keywords = "", referred = "[Berz1996b], [Fuchi1996a], [Kearfott2001a], [Pusch1996a]." } @INPROCEEDINGS{Berz1996a, author = "Martin Berz", editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank", year = 1996, title = "Calculus and Numerics on {Levi-Civita} Fields", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "19--35", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Berz1996a", crossref = "Berz1996c", abstract = "The formal process of the evaluation of derivatives using some of the various modern methods of computational differentiation can be recognized as an example for the application of conventional ``approximate'' numerical techniques on a non-archimedean extension of the real numbers. In many cases, the application of ``infinitely small'' numbers instead of ''small but finite'' numbers allows the use of the old numerical algorithm, but now with an error that in a rigorous way can be shown to become infinitely small (and hence irrelevant). While intuitive ideas in this direction have accompanied analysis from the early days of Newton and Leibniz, the first rigorous work goes back to Levi-Civita, who introduced a number field that in the past few years turned out to be particularly suitable for numerical problems. While Levi-Civita's field appears to be of fundamental importance and simplicity, efforts to introduce advanced concepts of calculus on it are only very new. In this paper, we address several of the basic questions providing a foundation for such a calculus. After addressing questions of algebra and convergence, we study questions of differentiability, in particular with an eye to usefulness for practical work.", comment = "", keywords = "Levi-Civita, Non-standard Analysis, Non-Archimedean Analysis, Analysis with Infinitesimals, Differentials, Infinitesimals, Derivatives as Differential Quotients, Computer Functions, Differential Quotients, Computation of Derivatives.", referred = "[Berz2001a], [Pusch1996a], [Shamseddine1996a]." } @INCOLLECTION{Berz1996b, author = "Martin Berz and Kyoko Makino and Khodr Shamseddine and Georg H. Hoffst{\"a}tter and Weishi Wan", editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank", year = 1996, title = "{COSY INFINITY} and Its Applications to Nonlinear Dynamics", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "363--365", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Berz1996b", crossref = "Berz1996c", abstract = "The Fortran-based environment COSY INFINTIY, as well as the related codes DAFOR and DAPRE, is presented. The codes contain modules for the computation of derivatives to very high orders in many variables, with a particular emphasis on sparsity. The main use of the code lies in the field of nonlinear dynamics, where it is used for the computation of perturbation expansions of Poincare maps to high orders as well as their analysis based on normal forms and other methods. Using Remainder Differential Algebraic Methods, quantitative and mathematically rigorous statements about long-term stability can be made for general systems. The code is currently used by more than 150 registered users, mostly in the field of beam physics for the study and design of particle accelerators.", comment = "", keywords = "COSY INFINITY, high-order derivatives, sparsity, nonlinear dynamics, differential algebra.", referred = "[Fuchi1996a], [Hoefkens2001a], [Kearfott2001a], [Makino2001a], [Shamseddine1996a]." } @BOOK{Berz1996c, editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank", year = 1996, title = "Computational Differentiation: Techniques, Applications, and Tools", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Berz1996c", abstract = "", comment = "", keywords = "", referred = "[Griewank2001a], [Klein2001a].", isbn = "0-89871-385-4" } @TECHREPORT{Berz1997a, author = "Martin Berz", month = "", year = 1997, title = "{COSY INFINITY} {V}ersion 8 Reference Manual", number = "MSUCL--1088", note = "See \url{cosy.nscl.msu.edu}", address = "Michigan State University, East Lansing, {MI} 48824", institution = "National Superconducting Cyclotron Laboratory", key = "Berz1997a", type = "", abstract = "", comment = "", keywords = "", referred = "[Makino2001a]." } @ARTICLE{Berz1998a, author = "Martin Berz and Georg H. Hoffst{\"a}tter", month = "", year = 1998, title = "Computation and Application of {T}aylor Polynomials with Interval Remainder Bounds", journal = "Reliable Computing", volume = 4, number = 1, pages = "83--97", note = "", key = "Berz1998a", abstract = "", comment = "", keywords = "", referred = "[Kearfott2001a]." } @ARTICLE{Berz1998b, author = "Martin Berz and Kyoko Makino", month = "", year = 1998, title = "Verified Integration of {ODE}s and Flows with Differential Algebraic Methods on {T}aylor Models", journal = "Reliable Computing", volume = 4, number = "", pages = "361--369", note = "", key = "Berz1998b", abstract = "", comment = "", keywords = "", referred = "[Makino2001a]." } @BOOK{Berz1999a, author = "Martin Berz", editor = "", year = 1999, title = "Modern Map Methods in Particle Beam Physics", series = "", number = "", note = "", publisher = "Academic Press", address = "San Diego", key = "Berz1999a", abstract = "", comment = "", keywords = "", referred = "[Hoefkens2001a], [Makino2001a].", isbn = "0-12-014750-5" } @ARTICLE{Berz1999b, author = "Martin Berz and Kyoko Makino", month = "", year = 1999, title = "New Methods for High-Dimensional Verified Quadrature", journal = "Reliable Computing", volume = 5, number = "", pages = "13--22", note = "", key = "Berz1999b", abstract = "", comment = "", keywords = "", referred = "[Makino2001a]." } @MISC{Berz2000a, author = "Martin Berz", month = "", year = 2000, title = "{COSY INFINITY} Web page", note = "See \url{cosy.nscl.msu.edu}", howpublished = "", key = "Berz2000a", abstract = "", comment = "", keywords = "", referred = "" } @INCOLLECTION{Berz2000c, author = "Martin Berz", month = "", year = 2000, title = "Analytical and Computational Methods for the {L}evi-{C}ivita Fields", booktitle = "Proc. Sixth International Conference on Nonarchimedean Analysis", volume = "", number = "", pages = "21--34", note = "", publisher = "Marcel Dekker", address = "New York", key = "Berz2000c", abstract = "", comment = "", keywords = "", referred = "[Berz2001a].", isbn = "0-8247-0611-0" } @INCOLLECTION{Berz2001a, author = "Martin Berz", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Towards a Universal Data Type for Scientific Computing", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 45, pages = "373--381", note = "", publisher = "Springer", address = "New York", key = "Berz2001a", crossref = "Corliss2001b", abstract = "Modern scientific computing uses an abundance of data types. Besides floating point numbers, we routinely use intervals, univariate Taylor series, Taylor series with interval coefficients, and more recently multivariate Taylor series. Newer are Taylor models, which allow verified calculations like intervals, but largely avoid many of their limitations, including the cancellation effect, dimensionality curse, and low-order scaling of resulting width to domain width. Another more recent structure is the Levi-Civita numbers, which allow viewing many aspects of scientific computation as an application of arithmetic and analysis with infinitely small numbers, and which are useful for a variety of purposes including the assessment of differentiability at branch points. We propose new methods based on partially ordered Levi-Civita algebras that allow for a unification of all these various approaches into one single data type.", comment = "", keywords = "", referred = "", isbn = "" } @INCOLLECTION{Berz2001b, author = "Martin Berz", editor = "", year = 2001, title = "Higher Order Verified Methods and Applications", booktitle = "Procedings of SCAN 2000", series = "", number = "", pages = "", note = "", publisher = "Kluwer Academic Publishers", address = "Dordrecht, Netherlands", key = "Berz2001b", abstract = "", comment = "", keywords = "", referred = "[Makino2001a]." } @ARTICLE{Berz2001c, author = "Martin Berz and Jens Hoefkens", month = "", year = 2001, title = "Verified Inversion of Functional Dependencies and Superconvergent Interval {N}ewton Methods", journal = "Reliable Computing", volume = 7, number = 5, pages = "", note = "", key = "Berz2001c", abstract = "", comment = "", keywords = "", referred = "[Hoefkens2001a]." } @ARTICLE{Berz2001d, author = "Martin Berz and Kyoko Makino and Jens Hoefkens", year = "2001, in print", title = "Verified Integration of Dynamics in the Solar System", journal = "Nonlinear Analysis", number = "", pages = "", key = "Berz2001d", abstract = "", comment = "", keywords = "", referred = "[Makino2001a]." } @ARTICLE{Bestle1983a, author = "Dieter Bestle and Michael Zeitz", year = 1983, title = "Canonical Form Observer Design for Non-Linear Time-Variable Systems", journal = "Int. J. Control", volume = 38, number = 2, pages = "419--431", key = "Bestle1983a", abstract = "", comment = "", keywords = "", referred = "[R{\"o}benack2001a]." } @TECHREPORT{Beulker1998a, author = "K.~Beulker", month = "", year = 1998, title = "{B}erechnung der {K}egelradzahngeometrie", number = 548, note = "", address = "", institution = "Forschungsvereinigung Antriebstechnik", key = "Beulker1998a", type = "FVA-Heft", abstract = "", comment = "", keywords = "", referred = "[Vogel2001a]." } @INPROCEEDINGS{Biros1999a, author = "George Biros and Omar Ghattas", editor = "", year = 1999, title = "Parallel {N}ewton-{K}rylov Methods for {PDE}-Constrained Optimization", booktitle = "Proceedings of SC99", series = "", number = "", pages = "", note = "", publisher = "IEEE Computer Society", address = "", key = "Biros1999a", abstract = "", comment = "", keywords = "", referred = "[Keyes2001a]." } @ARTICLE{Biros2000a, author = "George Biros and Omar Ghattas", month = "", year = 2000, title = "A {L}agrange-{N}ewton-{K}rylov-{S}chur Method for {PDE}-Constrained Optimization", journal = "SIAG/OPT Views-and-News", volume = 11, number = 2, pages = "1-6", note = "", key = "Biros2000a", abstract = "", comment = "", keywords = "", referred = "[Keyes2001a]." } @INCOLLECTION{Bischof1991a, author = "Christian H.~Bischof", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "Issues in Parallel Automatic Differentiation", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "100--113", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Bischof1991a", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "[Bischof1996b], [Christianson1996a], [Corliss1991a]; [Layne1991a], [Mancini2001a].", isbn = "0--89871--284--X" } @ARTICLE{Bischof1992c, author = "Christian H.~Bischof and Alan Carle and George F.~Corliss and Andreas Griewank and Paul D. Hovland", month = "", year = 1992, title = "{ADIFOR}: {G}enerating Derivative Codes from {F}ortran Programs", journal = "Scientific Programming", volume = 1, number = "", pages = "11--29", key = "Bischof1992c", abstract = "", comment = "", keywords = "", referred = "[Bischof1996b], [Bischof2001a], [Carle1996a], [Dignath2001a], [Eberhard1996a], [Klein1996a],[Park1996a], [Shiriaev1996a]." } @ARTICLE{Bischof1993b, author = "Christian H. Bischof and George F. Corliss and Andreas Griewank", month = "", year = 1993, title = "Structured Second- and Higher-Order Derivatives Through Univariate {T}aylor Series", journal = "Optimization Methods and Software", volume = 2, number = "", pages = "211--232", note = "", key = "Bischof1993b", abstract = "", comment = "Also appeared as Mathematics and Computer Science Division, Argonne National Laboratory Preprint MCS--P296--0392.", keywords = "", referred = "[Beley2001a], [Pusch1996a], [Rall1996a]." } @INPROCEEDINGS{Bischof1994c, author = "Christian H. Bischof and Larry Green and Ken Haigler and T. Knauff", year = 1994, title = "Calculation of Sensitivity Derivatives for Aircraft Design Using Automatic Differentiation", booktitle = "Proceedings of the 5th {AIAA/NASA/USAF/ISSMO} Symposium on Multidisciplinary Analysis and Optimization, AIAA 94-4261", pages = "73--84", note = "Also appeared as Argonne National Laboratory, Mathematics and Computer Science Division, Preprint MCS-P419-0294.", publisher = "American Institute of Aeronautics and Astronautics", key = "Bischof1994c", abstract = "", comment = "", keywords = "", referred = "[Bischof1996a], [Mancini2001a]." } @ARTICLE{Bischof1995f, author = "Christian Bischof and Peyvand Khademi and Ali Bouaricha and Alan Carle", month = "", year = 1996, title = "Efficient Computation of Gradients and {J}acobians by Dynamic Exploitation of Sparsity in Automatic Differentiation", journal = "Optim. Methods Software", volume = 7, number = "", pages = "1--39", note = "", key = "Bischof1995f", abstract = "", comment = "", keywords = "", referred = "[Mor\'e2001a]." } @INCOLLECTION{Bischof1996a, author = "Christian H.~Bischof and Alan Carle", editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank", year = 1996, title = "Users' Experience with {ADIFOR} 2.0", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "385--392", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Bischof1996a", crossref = "Berz1996c", abstract = "In July 1995, the ADIFOR~2.0 system for automatic differentiation of Fortran was made available to the academic and commercial communities via the World Wide Web. By January 1996, we had received and processed over one hundred requests for ADIFOR~2.0. In this paper, we describe some of the experiences of users of the system that should be interesting to developers of automatic differentiation tools.", comment = "", keywords = "ADIFOR, applications, experiences.", referred = "" } @INCOLLECTION{Bischof1996b, author = "Christian H.~Bischof and Mohammad R.~Haghighat", editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank", year = 1996, title = "Hierarchical Approaches to Automatic Differentiation", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "83--94", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Bischof1996b", crossref = "Berz1996c", abstract = "A mathematical function, specified by a computer program, can be differentiated efficiently through the exploitation of its program structure. The important properties of a program for the efficient generation of derivative code are the asymmetries between the number of inputs and outputs of program components at various levels of abstraction and the mathematical complexity of the involved operators. Automatic generation of efficient derivative codes thus requires analysis of programs for detection of such properties and systematic methods for their exploitation in composing the derivative codes. We suggest a hierarchical approach based on a partitioning of the computational or program graph as a means to deduce workable solutions to this hard problem. Each partition corresponds to a localized scope for derivative computation, and hierarchical partitions provide a mechanism for exploiting program structure at various levels. As a particular example, we discuss dynamic programming approaches for finding good one-dimensional partitions and generalizations to arbitrary directed acyclic graphs that, by recycling substructure information, allow one to determine the optimal elimination ordering for a graph with $n$ nodes with complexity $O(2^n)$, as compared with the $O(n!)$ complexity of a naive search. Lastly, we give a concrete example illustrating the hierarchical approach on the driven cavity problem from the MINPACK-2 optimization test set collection.", comment = "", keywords = "Differentiation partition, hybrid modes, optimal elimination ordering, higher-level operands, computational graph, program graph, hierarchical differentiation.", referred = "[Mancini2001a], [Naumann2001a], [Tadjouddine2001a]." } @ARTICLE{Bischof1996c, author = "Christian H.~Bischof and Alan Carle and Peyvand Khademi and Andrew Mauer", month = "", year = 1996, title = "{ADIFOR} 2.0: Automatic Differentiation of {F}ortran 77 Programs", journal = "IEEE Computational Science \& Engineering", volume = 3, number = 3, pages = "18--32", note = "", key = "Bischof1996c", abstract = "", comment = "Preprint MCS-P481-1194, Mathematics and Computer Science Division, Argonne National Laboratory, and CRPC-TR94491, Center for Research on Parallel Computation, Rice University.", keywords = "", referred = "[Abate2001a], [Bischof2001a], [Caillau2001a], [Kim2001a], [Mor\'e2001a], [Tijskens2001a]." } @ARTICLE{Bischof1997a, author = "Christian H.~Bischof and Lucas Roh and Andrew Mauer", month = "", year = 1997, title = "{ADIC} --- {An} Extensible Automatic Differentiation Tool for {ANSI-C}", journal = "Software--Practice and Experience", volume = 27, number = 12, pages = "1427--1456", note = "See \url{www-fp.mcs.anl.gov/division/software}.", key = "Bischof1997a", abstract = "", comment = "Also appeared as ANL/MCS-P626-1196 and CRCP-TR97676-S", keywords = "", referred = "[Abate2001a], [Dignath2001a], [Keyes2001a], [Lee2001a], [Mancini2001a], [Tijskens2001a]." } @ARTICLE{Bischof1997b, author = "Christian H.~Bischof and Peyvand M.~Khademi and A.~Bouaricha and Alan Carle", month = "", year = 1997, title = "Efficient Computation of Gradients and {J}acobians by Dynamic Exploitation of Sparsity in Automatic Differentiation", journal = "Optimization Methods and Software", volume = 7, number = "", pages = "1--39", note = "", key = "Bischof1997b", abstract = "", comment = "Also appeared as MCS--P519--0595", keywords = "", referred = "[Griewank2001a]." } @ARTICLE{Bischof1997c, author = "Christian H. Bischof and Ali Bouaricha and Peyvand Khademi and Jorge J. Mor{\'e}", month = "", year = 1997, title = "Computing Gradients in Large-Scale Optimization Using Automatic Differentiation", journal = "INFORMS J. Computing", volume = 9, number = "", pages = "185--194", note = "", key = "Bischof1997c", abstract = "", comment = "", keywords = "", referred = "[Mor\'e2001a]." } @TECHREPORT{Bischof1997d, author = "Christian H. Bischof and P. Wu", month = "", year = 1997, title = "Time-Parallel Computation of Pseudo-Adjoints for a Leapfrog Scheme", number = "MCS-P639-0197", note = "", address = "Argonne, Ill.", institution = "Argonne National Laboratory Mathematics and Computer Science Division", key = "Bischof1997d", type = "Preprint", abstract = "", comment = "", keywords = "", referred = "[Mancini2001a]." } @TECHREPORT{Bischof1998a, author = "Christian H. Bischof and Alan Carle and Paul D.~Hovland and Peyvand Khademi and Andrew Mauer", month = "", year = 1998, title = "{ADIFOR} 2.0 User's Guide ({Revision D})", number = "", note = "See \url{www.mcs.anl.gov/adifor}.", address = "", institution = "Mathematics and Computer Science Division Technical Memorandum no. 192 and Center for Research on Parallel Computation Technical Report CRPC-95516-S", key = "Bischof1998a", type = "", abstract = "", comment = "", keywords = "", referred = "[Charpentier2001a], [Forth2001a], [Giles2001a], [Klein2001a], [Mor\'e2001a], [Souli2001a], [Tadjouddine2001a]." } @MISC{Bischof1999a, author = "Christian H.~Bischof", month = "Dec.", year = 1999, title = "A Collection of Automatic Differentiation Tools", note = "See \url{www.mcs.anl.gov/autodiff/AD_Tools}", howpublished = "", key = "Bischof1999a", abstract = "", comment = "", keywords = "", referred = "[Bischof2001a]." } @MISC{Bischof1999b, author = "Christian H.~Bischof", month = "", year = 1999, title = "Availability of {ADIFOR} Software", note = "See \url{www.mcs.anl.gov/autodiff/ADIFOR}", howpublished = "", key = "Bischof1999b", abstract = "", comment = "", keywords = "", referred = "[Bischof2001a]." } @TECHREPORT{Bischof2000a, author = "Christian H.~Bischof and Martin B{\"u}cker and Paul D.~Hovland", month = "", year = 2000, title = "On Combining Computational Differentiation and Toolkits for Parallel Scientific Computing", number = "ANL/MCS-P797-0200", note = "In Proceedings of EuroPar 2000, Springer LNCS 1900, p. 86--94.", address = "", institution = "Mathematics and Computer Science Division, Argonne National Laboratory", key = "Bischof2000a", type = "", abstract = "", comment = "", keywords = "", referred = "[Lee2001a]." } @INCOLLECTION{Bischof2001a, author = "Christian H.~Bischof and H.~Martin B{\"u}cker and Dieter {an Mey}", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "A Case Study of Computational Differentiation Applied to Neutron Scattering", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 6, pages = "69--74", note = "", publisher = "Springer", address = "New York", key = "Bischof2001a", crossref = "Corliss2001b", abstract = "In a neutron scattering application, an unconstrained nonlinear minimization problem is used for the fitting of model parameters to experimental data. Automatic differentiation enables, in a completely mechanical fashion, algorithmic changes by switching from a quasi-Newton method, where first order derivatives are approximated by finite differences, to a modified Gauss--Newton method using exact first order derivatives. Compared to the original code, the code generated by this black box approach produces reliable results rather than results of dubious quality. This approach also is faster in terms of execution time. Its performance is improved further by replacing the most time-consuming subroutine involved in the derivative evaluation by a surprisingly simple, hand-coded implementation of the corresponding analytic expression.", comment = "", keywords = "", referred = "[Klein2001a].", isbn = "" } @INCOLLECTION{Blanch1998a, author = "Joakim O. Blanch and William W. Symes and Roelof Versteeg", editor = "Robert G. Keys and Douglas J. Foster", year = 1998, title = "A Numerical Study of Linear Viscoacoustic Inversion", booktitle = "Comparison of Seismic Inversion Methods on a Single Real Data Set", series = "", number = "", pages = "13--44", note = "", publisher = "Society of Exploration Geophysicists", address = "Tulsa, Oklahoma, USA", key = "Blanch1998a", abstract = "", comment = "", keywords = "", referred = "[Gockenbach2001a]." } @TECHREPORT{Bock1987a, author = "H.~G.~Bock", month = "", year = 1987, title = "Randwertprobleme zur {P}arameteridentifizierung in {S}ystemen Nichtlinearer {D}ifferentialgleichungen", number = 183, note = "", address = "", institution = "Universit{\"a}t Bonn", key = "Bock1987a", type = "Bonner Mathematische Schriften", abstract = "", comment = "", keywords = "", referred = "[Klein2001a]." } @INPROCEEDINGS{Bodin1998a, author = "Fran{\c c}ois Bodin and Y. M{/'e}vel and R. Quiniou", editor = "", year = 1998, title = "A User Level Program Transformation Tool", booktitle = "Proceedings of the International Conference on Supercomputing (Melbourne, Australia)", series = "", number = "", pages = "", note = "", publisher = "", address = "", key = "Bodin1998a", abstract = "", comment = "", keywords = "", referred = "[Bodin2001a]." } @INCOLLECTION{Bodin2001a, author = "Fran{\c c}ois Bodin and Antoine Monsifrot", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Performance Issues in Automatic Differentiation on Superscalar Processors", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 4, pages = "51--57", note = "", publisher = "Springer", address = "New York", key = "Bodin2001a", crossref = "Corliss2001b", abstract = "We overview code optimizations for superscalar processors (Pentium, Ultra Sparc, Alpha, etc.) in the context of automatic differentiation. Using an example we show the impact of program transformations used to increase code efficiency.", comment = "", keywords = "", referred = "", isbn = "" } @MISC{Borggaard2000a, author = "Jeff Borggaard and Arun Verma", month = "", year = 2000, title = "An {AD} Technique for Computing Approximations to the Continuous Sensitivity Equation", note = "", howpublished = "Presented at the Third International Conference on Automatic Differentiation (Nice)", key = "Borggaard2000a", abstract = "", comment = "", keywords = "", referred = "[Caillau2001a]." } @ARTICLE{Bouaricha1997a, author = "Ali Bouaricha and Jorge J. Mor{\'e}", month = "", year = 1997, title = "Impact of Partial Separability on Large-Scale Optimization", journal = "Comp. Optim. Appl.", volume = 7, number = 1, pages = "27--40", note = "", key = "Bouaricha1997a", abstract = "", comment = "", keywords = "", referred = "[Mor\'e2001a]." } @INCOLLECTION{Braconnier2001a, author = "Thierry Braconnier and Philippe Langlois", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "From Rounding Error Estimation to Automatic Correction with {AD}", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 42, pages = "351--357", note = "", publisher = "Springer", address = "New York", key = "Braconnier2001a", crossref = "Corliss2001b", abstract = "Using automatic differentiation (AD) to estimate the propagation of rounding errors in numerical algorithms is classic. We propose a new application of AD to roundoff analysis providing an automatic correction of the first order effect of the elementary rounding errors. We present the main characteristics of this method and significant examples of its application to improve the accuracy of computed results and/or the stability of the algorithm.", comment = "", keywords = "", referred = "", isbn = "" } @BOOK{Brezinski1980a, author = "Claude Brezinski", editor = "", year = 1980, title = "Pad{\'e} Type Approximation and General Orthogonal Polynomials", series = "", number = "", note = "", publisher = "Birkh{\"a}user Verlag", address = "", key = "Brezinski1980a", abstract = "", comment = "", keywords = "", referred = "[Beley2001a].", isbn = "" } @ARTICLE{Brown1990a, author = "Peter N. Brown and Youcef Saad", month = "", year = 1990, title = "Hybrid {K}rylov Methods for Nonlinear Systems of Equations", journal = "SIAM J. Sci. Stat. Comput.", volume = 11, number = 3, pages = "450--481", note = "", key = "Brown1990a", abstract = "", comment = "", keywords = "", referred = "[Keyes2001a]." } @TECHREPORT{Brown2000a, author = "Peter N. Brown and C. S. Woodward", month = "", year = 2000, title = "Preconditioning Strategies for Fully Implicit Radiation Diffusion with Material-Energy Transfer", number = "UCRL--JC--139087", note = "", address = "", institution = "Lawrence Livermore National Laboratory", key = "Brown2000a", type = "", abstract = "", comment = "Submitted to {\em SIAM J. Sci. Comput.}", keywords = "", referred = "[Keyes2001a]." } @ARTICLE{Byrd1994a, author = "Richard H. Byrd and Jorge Nocedal and Robert B. Schnabel", month = "", year = 1994, title = "Representations of Quasi-{N}ewton Matrices and their Use in Limited-Memory Methods", journal = "Math. Prog., Ser. A", volume = 63, number = "", pages = "129--156", note = "", key = "Byrd1994a", abstract = "", comment = "", keywords = "", referred = "[Keyes2001a]." } @ARTICLE{Byrne1999a, author = "George D.~Byrne and Alan C.~Hindmarsh", month = "", year = 1999, title = "{PVODE}, An {ODE} Solver for Parallel Computers", journal = "Int.~J.~High Perf.~Comput.~Appl.", volume = 13, number = "", pages = "354--365", note = "", key = "Byrne1999a", abstract = "", comment = "", keywords = "", referred = "[Lee2001a]." } @TECHREPORT{Cai1989a, author = "Xiao-Chuan Cai", month = "", year = 1989, title = "Some Domain Decomposition Algorithms for Nonselfadjoint Elliptic and Parabolic Partial Differential Equations", number = 461, note = "", address = "New York", institution = "Courant Institute", key = "Cai1989a", type = "{T}echnical {R}eport", abstract = "", comment = "", keywords = "", referred = "[Keyes2001a]." } @ARTICLE{Cai1994a, author = "Zhiqiang Cai and Raytcho D. Lazarov and Thomas A. Manteuffel and Stephen F. McCormick", month = "", year = 1994, title = "First-Order Least Squares for Partial Differential Equations: {P}art {I}", journal = "SIAM J. Numer. Anal.", volume = 31, number = "", pages = "1785--1799", note = "", key = "Cai1994a", abstract = "", comment = "", keywords = "", referred = "[Tijskens2001a]." } @ARTICLE{Cai1997a, author = "Zhiqiang Cai and Thomas A. Manteuffel and Stephen F. McCormick", month = "", year = 1997, title = "First-Order Least Squares for Partial Differential Equations: {P}art {II}", journal = "SIAM J. Numer. Anal.", volume = 34, number = "", pages = "425--454", note = "", key = "Cai1997a", abstract = "", comment = "", keywords = "", referred = "[Tijskens2001a]." } @ARTICLE{Cai2000a, author = "Xiao-Chuan Cai and David E. Keyes", month = "", year = "2000, submitted", title = "Nonlinearly Preconditioned Inexact {N}ewton Algorithms", journal = "SIAM J. Sci. Comput.", volume = "", number = "", pages = "", note = "See \url{www.icase.edu/~keyes/papers/aspin.pdf}.", key = "Cai2000a", abstract = "", comment = "", keywords = "", referred = "[Keyes2001a]." } @TECHREPORT{Caillau1998a, author = "Jean-Baptiste Caillau and Joseph Gergaud and Joseph Noailles", month = "July", year = 1998, title = "Trajectoires optimales \`a pouss\'ee continue", number = "R \& T A3006", note = "(in French)", address = "", institution = "CNES (French Space Agency) / ENSEEIHT--IRIT", key = "Caillau1998a", type = "Contract Report", abstract = "", comment = "", keywords = "", referred = "[Caillau2001a]." } @TECHREPORT{Caillau2000a, author = "Jean-Baptiste Caillau and Joseph Noailles", month = "March", year = 2000, title = "Geometric Study of Time Optimal Orbit Transfer", number = "RT/APO/00/1", note = "", address = "", institution = "ENSEEIHT-IRIT", key = "Caillau2000a", type = "{T}echnical {R}eport", abstract = "", comment = "", keywords = "", referred = "[Caillau2001a]." } @INPROCEEDINGS{Caillau2000b, author = "Jean-Baptiste Caillau and Joseph Noailles", editor = "", year = 2000, title = "Wavelets for Adaptive Solution of Boundary Value Problems", booktitle = "Proceedings of the 16th IMACS World Congress", series = "", number = "", pages = "", note = "", publisher = "", address = "Lausanne, Switzerland", key = "Caillau2000b", abstract = "", comment = "", keywords = "", referred = "[Caillau2001a]." } @INPROCEEDINGS{Caillau2000c, author = "Jean-Baptiste Caillau", editor = "", year = 2000, title = "Continuation Technique for a Weakly Controlled Satellite", booktitle = "Nonlinear Analysis 2000", series = "", number = "", pages = "", note = "Invited poster session", publisher = "", address = "New-York", key = "Caillau2000c", abstract = "", comment = "", keywords = "", referred = "[Caillau2001a]." } @INCOLLECTION{Caillau2001a, author = "Jean-Baptiste Caillau and Joseph Noailles", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Optimal Control Sensitivity Analysis with {AD}", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 11, pages = "109-115", note = "", publisher = "Springer", address = "New York", key = "Caillau2001a", crossref = "Corliss2001b", abstract = "In order to apply a parametric method to a minimum time control problem in celestial mechanics, a sensitivity analysis is performed. The analysis is continuous in the sense that it is done in the infinite dimensional control setting. The resulting sufficient second order condition is evaluated by means of automatic differentiation, while the associated sensitivity derivative is computed by continuous reverse differentiation. The numerical results are given for several examples of orbit transfer, also illustrating the advantages of automatic differentiation over finite differences for the computation of gradients on the discretized problem.", comment = "", keywords = "", referred = "", isbn = "" } @ARTICLE{Caillau2001b, author = "Jean-Baptiste Caillau and Joseph Noailles", month = "", year = 2001, title = "Sensitivity Analysis for Time Optimal Orbit Transfer", journal = "Optimization", volume = 49, number = 4, pages = "327--350", note = "", key = "Caillau2001b", abstract = "In order to apply a parametric method to a minimum time control problem in celestial mechanics, a sensitivity analysis is performed. The analysis is continuous in the sense that it is done in the infinite dimensional control setting. The resulting sufficient second order condition is evaluated by means of automatic differentiation, while the associated sensitivity derivative is computed by continuous reverse differentiation. The numerical results are given for several examples of orbit transfer, also illustrating the advantages of automatic differentiation over finite differences for the computation of gradients on the discretized problem.", comment = "", keywords = "", referred = "[Caillau2001a]." } @INCOLLECTION{Campbell1996a, author = "Stephen L.~Campbell and Richard Hollenbeck", editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank", year = 1996, title = "Automatic Differentiation and Implicit Differential Equations", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "215--227", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Campbell1996a", crossref = "Berz1996c", abstract = "Many physical processes are most naturally and easily modeled as mixed systems of differential and algebraic equations (DAEs). There has been an increased interest in several areas in exploiting the advantages of working directly with these implicit models. Differentiation plays an important role in both the analysis and numerical solution of DAEs. Automatic differentiation can have a significant impact on what is considered a practical approach and what types of problems can be solved. However, working with DAEs places special demands on automatic differentiation codes. More is required than just computing a gradient quickly. This paper will begin with a brief introduction to DAEs and how differentiation is important when working with DAEs. Then the requirements in terms of both information and performance that DAEs make of automatic differentiation software will be presented. Some of our own experience in using automatic differentiation software will be mentioned. It will be seen that automatic differentiation software has a significant role to play in the future for DAEs but that not all of the demands that the numerical solution of DAEs places on automatic differentiation software are currently being met.", comment = "", keywords = "Differential algebraic equations, numerical integrators, higher derivatives.", referred = "" } @INCOLLECTION{Cappelaere2001a, author = "Bernard Cappelaere and David Elizondo and Christ{\`e}le Faure", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Odyss{\'e}e versus Hand Differentiation of a Terrain Modelling Application", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 7, pages = "75--82", note = "", publisher = "Springer", address = "New York", key = "Cappelaere2001a", crossref = "Corliss2001b", abstract = "A comparison is made between differentiation alternatives for a terrain modeling problem, a sample application where strong non-linearities are solved iteratively. Investigated methods include automatic differentiation (AD) with the \odyssee\ software (forward and reverse modes) and manual differentiation (MD) using the model's adjoint equations. The comparison mainly focuses on accuracy and computing efficiency, as well as on development effort. While AD ensures perfect consistency between the computer model and its derivative at a low development cost, MD shows significantly lesser computing costs. We discuss the perturbation method as well as hybrid strategies that combine advantages of AD and MD.", comment = "", keywords = "", referred = "", isbn = "" } @INCOLLECTION{Carle1996a, author = "Alan Carle and Mike Fagan", editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank", year = 1996, title = "Improving Derivative Performance for {CFD} by Using Simplified Recurrences", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "343--351", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Carle1996a", crossref = "Berz1996c", abstract = "Many scientific programs generate solutions to partial differential equations by using an iterative process to reduce a residual quantity. Straightforward differentiation of these programs yields an iterative recurrence that involves both the derivative of the residual, and the derivative of the original process. For a certain class of these problems, the derivative recurrence can be {\em simplified\/} to avoid computing the derivative of the original process. A program implementing a simplified recurrence should run faster than its fully differentiated counterpart, since it avoids the redundant computation. In this paper we demonstrate a method for using automatic differentiation tools to facilitate the production of simplified derivative recurrence programs. We illustrate our technique by constructing and validating a simplified derivative version of the OVERFLOW computational fluid dynamics program using the ADIFOR automatic differentiation tool.", comment = "", keywords = "Simplified recurrence, incremental iterative, CFD, OVERFLOW, ADIFOR.", referred = "" } @MISC{Carle1997a, author = "Alan Carle", month = "", year = 1997, title = "", note = "", howpublished = "Personal communication", key = "Carle1997a", abstract = "", comment = "", keywords = "", referred = "[Abate2001a]." } @TECHREPORT{Carle1998a, author = "Alan Carle and Mike Fagan and Larry L. Green", month = "", year = 1998, title = "Preliminary Results from the Application of Automated Code Generation to {CFL3D}", number = "Paper 98-4807", note = "", address = "", institution = "AIAA", key = "Carle1998a", type = "Conference paper", abstract = "", comment = "", keywords = "", referred = "[Giles2001a]." } @TECHREPORT{Carle2000b, author = "Alan Carle and Mike Fagan", month = "", year = 2000, title = "{ADIFOR} 3.0 Overview", number = "CAAM-TR-00-02", note = "", address = "", institution = "Rice University", key = "Carle2000b", type = "", abstract = "", comment = "", keywords = "", referred = "[Carle2001a]." } @INCOLLECTION{Carle2001a, author = "Alan Carle and Mike Fagan", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Automatically Differentiating {MPI-1} Datatypes: {T}he Complete Story", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 25, pages = "215--222", note = "", publisher = "Springer", address = "New York", key = "Carle2001a", crossref = "Corliss2001b", abstract = "This chapter describes the problems met while extending ADIFOR 3.0 to handle programs coming from the MPI datatypes. To give a complete picture of the design space, the paper first explains why creating a differentiated interface for MPI is preferable to differentiating MPI source itself. Next, we identify the two main problems that MPI datatypes present and present two potential solution techniques. In conclusion, we give some preliminary implementation results.", comment = "", keywords = "", referred = "", isbn = "" } @MISC{Carroll1999a, author = "David L. Carroll", month = "March", year = 1999, title = "{FORTRAN} Genetic Algorithm Driver", note = "See \url{www.staff.uiuc.edu/~carroll/ga.html}", howpublished = "", key = "Carroll1999a", abstract = "", comment = "", keywords = "", referred = "[Ben-Haj-Yedder2001a]." } @MISC{Casanova2000a, author = "Daniele Casanova", month = "December", year = 2000, title = "Performance Optimisation of Formula One Cars", note = "", howpublished = "Talk presented at Technical University Dresden", key = "Casanova2000a", abstract = "", comment = "", keywords = "", referred = "[Klein2001a]." } @INCOLLECTION{Casanova2001a, author = "Daniele Casanova and Robin S.~Sharp and Mark Final and Bruce Christianson and Pat Symonds", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Application of Automatic Differentiation to Race Car Performance Optimisation", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 12, pages = "117--124", note = "", publisher = "Springer", address = "New York", key = "Casanova2001a", crossref = "Corliss2001b", abstract = "A formal method for the evaluation of the minimum time vehicle manoeuvre is described. The problem is treated as one of optimal control and is solved using a direct transcription method. The resulting non-linear programming problem is solved using the sequential quadratic programming algorithm SNOPT for constrained optimisation. The automatic differentiation software tool \textbf{AD}\raisebox{-.25ex}{\textsl{opt}} is used for the evaluation of the first-order derivatives of objective and constraint functions with respect to the control variables. The implementation of automatic differentiation is more robust and ten times as fast compared to the use of a finite difference determination of the Jacobian.", comment = "", keywords = "", referred = "[Caillau2001a].", isbn = "" } @ARTICLE{Chang1982a, author = "Y. F. Chang and George F. Corliss", month = "", year = 1982, title = "Solving Ordinary Differential Equations Using {T}aylor Series", journal = "ACM Trans. Math. Software", volume = 8, number = "", pages = "114--144", note = "", key = "Chang1982a", abstract = "A Fortran pre-processor program uses automatic differentiation to write a Fortran object program which is then run to solve the system. Parts: \begin{enumerate} \item Expand the series using recurrence relations. \item Estimate the radius of convergence of each component. \item Select a step size by comparison with series for model problems. \item Extend the solution by analytic continuation. \end{enumerate} The series analysis provides valuable information about analytic properties of the solution like the location and order of primary singularities. Taylor series methods are shown to be competitive with DVERK and DGEAR in terms of speed and accuracy.", comment = "", keywords = "point algorithm; Taylor series; radius of convergence; pre-processing; automatic differentiation.", referred = "[Hoefkens2001a], [Rall1996a]." } @ARTICLE{Chang1994a, author = "Y. F. Chang and George F. Corliss", month = "", year = 1994, title = "{ATOMFT}: {S}olving {ODE}s and {DAE}s Using {T}aylor Series", journal = "Computers and Mathematics with Applications", volume = 28, number = "", pages = "209--233", note = "", key = "Chang1994a", abstract = "", comment = "", keywords = "", referred = "[Hoefkens2001a], [Rall1996a]." } @ARTICLE{Chapman1994a, author = "W.~L.~Chapman and W.~J.~Welch and K.~P.~Bowman and J.~Sacks and J.~E.~Walsh", month = "", year = 1994, title = "Arctic Sea-Ice Variability: {M}odel Sensitivities and a Multidecadal Simulation", journal = "J.~Geophys.~Res.", volume = 99, number = "", pages = "919--935", note = "", key = "Chapman1994a", abstract = "", comment = "", keywords = "", referred = "[Kim2001a]." } @INCOLLECTION{Char1991a, author = "Bruce W.~Char", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "Computer Algebra as a Toolbox for Program Generation and Manipulation", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "53--60", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Char1991a", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "[Garc91a], [Gold91a], [Irim91a].", isbn = "0--89871--284--X" } @INCOLLECTION{Charpentier2001a, author = "Isabelle Charpentier and No{\"e}l Jakse and Fabrice Veers{\'e}", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Second Order Exact Derivatives to Perform Optimization on Self-Consistent Integral Equations Problems", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 22, pages = "189--195", note = "", publisher = "Springer", address = "New York", key = "Charpentier2001a", crossref = "Corliss2001b", abstract = "Great efforts have been made to search for enhanced semi-empirical forms of the bridge function $b$ appearing in disordered condensed matter problems which are solved using the integral equation method. Currently, parameterized forms of the bridge function are manually chosen to fit as closely as possible the thermodynamic self-consistent equations depending on $g$ and its derivatives. The paper discusses a second-order differentiation of the computer code that enables construction of parameterized bridge functions using optimal control techniques.", comment = "", keywords = "", referred = "[Forth2001a], [Klein2001a].", isbn = "" } @ARTICLE{Charpentier2001b, author = "Isabelle Charpentier and No{\"e}l Jakse", month = "", year = 2001, title = "Exact Derivatives of the Pair-Correlation Function of Simple Liquids Using the Tangent Linear Method", journal = "J.~Chem.~Phys", volume = 114, number = "", pages = "2284--2292", note = "", key = "Charpentier2001b", abstract = "", comment = "", keywords = "", referred = "[Charpentier2001a]." } @INCOLLECTION{Chavent1996a, author = "Guy Chavent and J{\'e}r{\^o}me Jaffr{\'e} and Sophie J{\'e}gou and Jun Liu", editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank", year = 1996, title = "A Symbolic Code Generator for Parameter Estimation", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "129--136", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Chavent1996a", crossref = "Berz1996c", abstract = "GRADJ, a symbolic code generator (SCG), based on the Symbolic Computation System Maple, is described. Given discretized PDE's and a discrete data misfit function, it generates two Fortran codes. One computes the data misfit function, and the other computes its gradient. The performance of the generated codes for estimating parameters for flow in porous media is examined.", comment = "", keywords = "Parameter estimation, symbolic code generator, Maple, adjoint state method, flow in porous media.", referred = "" } @ARTICLE{Christianson1991b, author = "Bruce Christianson", year = 1991, title = "Reverse Accumulation and Accurate Rounding Error Estimates for {T}aylor Series Coefficients", journal = "Optimization Methods and Software", volume = 1, number = 1, pages = "81--94", note = "Also appeared as Tech. Report No. NOC TR239, The Numerical Optimisation Centre, University of Hertfordshire, U.K., July 1991", key = "Christianson1991b", abstract = "", comment = "", keywords = "", referred = "[R{\"o}benack2001a], [Shirieav1996a]." } @ARTICLE{Christianson1994a, author = "Bruce Christianson", month = "", year = 1994, title = "Reverse Accumulation and Attractive Fixed Points", journal = "Optimization Methods and Software", volume = 3, number = "", pages = "311--326", key = "Christianson1994a", abstract = "", comment = "Also appeared as The Numerical Optimisation Centre, University of Hertfordshire Tech. Report No. NOC TR 258, Hatfield, UK, March, 1992.", keywords = "", referred = "[Christianson1996a], [Giering1997a], [Giles2001a], [Mohammadi1996a], [Rall1996a]." } @INCOLLECTION{Christianson1996a, author = "Bruce Christianson and Laurence C.~W.~Dixon and Steven Brown", editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank", year = 1996, title = "Sharing Storage Using Dirty Vectors", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "107--115", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Christianson1996a", crossref = "Berz1996c", abstract = "Consider a computation $F$ with $n$ inputs (independent variables) and $m$ outputs (dependent variables), and suppose that we wish to evaluate the Jacobian of $F$. Automatic differentiation commonly performs this evaluation by associating vector storage either with the program variables (in the case of forward-mode automatic differentiation) or with the adjoint variables (in the case of reverse). Each vector component contains a partial derivative with respect to an independent variable, or a partial derivative of a dependent variable, respectively. The vectors may be full vectors, or they may be dynamically managed sparse data structures. In either case, many of these vectors will be scalar multiples of one another. For example, any intermediate variable produced by a unary operation in the forward mode will have a derivative vector that is a multiple of the derivative for the argument. Any computational graph node that is read just once during its lifetime will have an adjoint vector that is a multiple of the adjoint of the node that reads it. It is frequently wasteful to perform component multiplications explicitly. A scalar multiple of another vector can be replaced by a single multiplicative ``scale factor'' together with a pointer to the other vector. Automated use of this ``dirty vector'' technique can save considerable memory management overhead and dramatically reduce the number of floating-point operations required. In particular, dirty vectors often allow shared threads of computation to be reverse-accumulated cheaply. The mechanism permits a number of generalizations, some of which give efficient techniques for preaccumulation.", comment = "", keywords = "Computational graph, copy-on-write, Jacobian, preaccumulation, reducing FLOP count, sparse vectors.", referred = "[Geitner1996a], [Utke1996a]." } @ARTICLE{Christianson1998a, author = "Bruce Christianson", month = "", year = 1998, title = "Reverse Accumulation and Implicit Functions", journal = "Optimization Methods and Software", volume = 9, number = 4, pages = "307--322", note = "", key = "Christianson1998a", abstract = "", comment = "", keywords = "", referred = "[Giles2001a]." } @ARTICLE{Christianson1999a, author = "Bruce Christianson", month = "", year = 1999, title = "Automatic Differentiation and {P}antoja's Algorithm", journal = "Optimization Methods and Software", volume = 10, number = 1, pages = "729--743", note = "", key = "Christianson1999a", abstract = "", comment = "", keywords = "", referred = "[Christianson2001a]." } @MISC{Christianson1999b, author = "Bruce Christianson and Andreas Griewank and Uwe Naumann", month = "", year = 1999, title = "Automated Analysis and Enhancement of Applications Code", note = "", howpublished = "Pre-proposal submitted to the European Science Foundation", key = "Christianson1999a", abstract = "", comment = "", keywords = "", referred = "[Hague2001a]." } @INCOLLECTION{Christianson2001a, author = "Bruce Christianson and Michael C.~Bartholomew-Biggs", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Globalization of {P}antoja's Optimal Control Algorithm", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 13, pages = "125--130", note = "", publisher = "Springer", address = "New York", key = "Christianson2001a", crossref = "Corliss2001b", abstract = "In 1983 Pantoja described a stagewise construction of the Newton direction for a general class of discrete time optimal control problems. His algorithm incurs amazingly low overheads: the cost (measured in target function evaluations) is independent of the number of discrete time-steps. The algorithm can be modified to verify that the Hessian contains no eigenvalues less than a postulated quantity, and to produce an appropriate descent direction in the case where the Hessian fails to be positive definite and global convergence becomes an issue. Coleman and Liao have proposed a specific damping strategy in this context. Here we describe how automatic differentiation can be used to implement Pantoja's algorithm, and we briefly consider some alternative globalization strategies, within which AD techniques can be further deployed.", comment = "", keywords = "", referred = "", isbn = "" } @ARTICLE{Coleman1983a, author = "Thomas F.~Coleman and Jorge J.~Mor{\'e}", month = "", year = 1983, title = "Estimation of Sparse {J}acobian Matrices and Graph Coloring Problems", journal = "SIAM J. Numer. Anal.", volume = 20, number = 1, pages = "187--209", key = "Coleman1983a", abstract = "", comment = "", keywords = "", referred = "[Coleman1996a], [Geitner1996a], [Abate2001a]." } @ARTICLE{Coleman1984a, author = "Thomas F. Coleman and Burton S. Garbow and Jorge J. Mor{\'e}", month = "", year = 1984, title = "Software for Estimating Sparse {J}acobian Matrices", journal = "ACM Trans. Math. Software", volume = 10, number = 3, pages = "329--345", key = "Coleman1984a", abstract = "", comment = "", keywords = "", referred = "[Coleman1996a], [Hossain2001a], [Mor\'e2001a]." } @ARTICLE{Coleman1984b, author = "Thomas F. Coleman and Jorge J. Mor{\'e}", month = "", year = 1984, title = "Estimation of Sparse {H}essian Matrices and Graph Coloring Problems", journal = "Math. Programming", volume = 28, number = "", pages = "243--270", key = "Coleman1984b", abstract = "", comment = "", keywords = "", referred = "[Coleman1996a], [Mor\'e2001a]." } @ARTICLE{Coleman1985a, author = "Thomas F. Coleman and Burton S. Garbow and Jorge J. Mor{\'e}", month = "", year = 1985, title = "Software for Estimating Sparse {H}essian Matrices", journal = "ACM Trans. Math. Software", volume = 11, number = 4, pages = "363--377", key = "Coleman1985a", abstract = "", comment = "", keywords = "", referred = "[Coleman1996a], [Mor\'e2001a]." } @ARTICLE{Coleman1986a, author = "Thomas F. Coleman and Jin-Yi Cai", month = "", year = 1986, title = "The Cyclic Coloring Problem and Estimation of Sparse {H}essian Matrices", journal = "SIAM J. Alg. Disc. Meth.", volume = 7, number = 2, pages = "221--235", note = "", key = "Coleman1986a", abstract = "", comment = "", keywords = "", referred = "[Hossain2001a], [Mor\'e2001a]." } @ARTICLE{Coleman1995a, author = "Thomas F.~Coleman and Aiping Liao", month = "", year = 1995, title = "An Efficient Trust Region Method for Unconstrained Discrete-Time Optimal Control Problems", journal = "Computational Optimization and Applications", volume = 4, number = "", pages = "47--66", key = "Coleman1995a", abstract = "", comment = "", keywords = "", referred = "[Christianson2001a]." } @INCOLLECTION{Coleman1996a, author = "Thomas F.~Coleman and Arun Verma", editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank", year = 1996, title = "Structure and Efficient {J}acobian Calculation", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "149--159", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Coleman1996a", crossref = "Berz1996c", abstract = "Many computational tasks require the determination of the Jacobian matrix, at a given argument, for a large nonlinear system of equations. Calculation or approximation of a Newton step is a related task. The development of robust automatic differentiation (AD) software allows for ``painless'' and accurate calculation of these quantities; however, straightforward application of AD software on large-scale problems can require an inordinate amount of computation. Fortunately, large-scale systems of nonlinear equations typically exhibit either sparsity or structure in their Jacobian matrices. In this paper, we proffer general approaches for exploiting sparsity and structure to yield efficient ways to determine Jacobian matrices (and Newton steps) via automatic differentiation.", comment = "", keywords = "Newton step, Jacobian structure, Jacobian sparsity.", referred = "[Griewank2001a], [Hossain2001a]." } @ARTICLE{Coleman1998a, author = "Thomas F. Coleman and Arun Verma", month = "", year = 1998, title = "The Efficient Computation of Sparse {J}acobian Matrices Using Automatic Differentiation", journal = "SIAM J. Sci. Comput.", volume = 19, number = 4, pages = "1210--1233", key = "Coleman1998a", abstract = "", comment = "", keywords = "", referred = "[Hossain2001a]." } @TECHREPORT{Coleman1998b, author = "Thomas F.~Coleman and Arun Verma", month = "", year = 1998, title = "{ADMAT}: An Automatic Differentiation Toolbox for {MATLAB}", number = "", note = "", address = "", institution = "Computer Science Department, Cornell University", key = "Coleman1998b", type = "", abstract = "", comment = "", keywords = "", referred = "[Keyes2001a]." } @ARTICLE{Coleman2000a, author = "Thomas F. Coleman and Arun Verma", month = "", year = 2000, title = "{ADMIT-1}: {A}utomatic Differentiation and {MATLAB} Interface Toolbox", journal = "ACM Trans. Math. Softw.", volume = 26, number = 1, pages = "150--175", key = "Coleman2000a", abstract = "", comment = "", keywords = "", referred = "" } @TECHREPORT{Colony1993a, author = "R.~L.~Colony and I.~Rigor", month = "", year = 1993, title = "International {A}rctic Buoy Program Data Report for 1 {J}anuary 1992 31 {D}ecember 1992", number = "APL-UW TM29-93", note = "", address = "Seattle", institution = "Appl. Phys.~Lab., Univ.~of Washington", key = "Colony1993a", type = "Tech. Memo.", abstract = "", comment = "", keywords = "", referred = "[Kim2001a]." } @ARTICLE{Conforti2001a, author = "D. Conforti and Marco Mancini", month = "", year = 2001, title = "A Curvilinear Search Algorithm for Unconstrained Optimization by Automatic Differentiation", journal = "Optimization Methods and Software", volume = "15r", number = "3-4", pages = "283--297", key = "Conforti2001a", abstract = "", comment = "", keywords = "", referred = "[Christianson2001a]." } @INCOLLECTION{Corliss1991a, author = "George F.~Corliss", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "Overloading Point and Interval {T}aylor Operators", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "139--146", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Corliss1991a", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "[Jued91a], [Kalm91a], [Layn91a].", isbn = "0--89871--284--X" } @INCOLLECTION{Corliss1991d, author = "George F.~Corliss", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "Automatic Differentiation Bibliography", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "331--353", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Corliss1991d", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "", isbn = "0--89871--284--X" } @TECHREPORT{Corliss1992d, author = "George F.~Corliss", month = "", year = 1992, title = "{ADIFOR} Case Study : {VODE + ADIFOR}", number = "ANL/MCS--TM--168", address = "Argonne, Ill.", institution = "Mathematics and Computer Science Division, Argonne National Laboratory", key = "Corliss1992d", type = "Technical Memorandum", abstract = "", comment = "", keywords = "", referred = "[Rall1996a], [Lee2001a]." } @MISC{Corliss1998a, author = "George F. Corliss", month = "", year = 1998, title = "GlobSol Entry Page", note = "See \url{www.mscs.mu.edu/~globsol}", howpublished = "", key = "Corliss1998a", abstract = "", comment = "", keywords = "", referred = "[Kearfott2001a]." } @INCOLLECTION{Corliss2001a, author = "George F.~Corliss", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Automatic Differentiation Bibliography", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 46, pages = "383--425", note = "", publisher = "Springer", address = "New York", key = "Corliss2001a", crossref = "Corliss2001b", abstract = "This is a bibliography of work related to automatic differentiation. It represents the compilation of all works cited by all chapters in this volume, {\sl Automatic Differentiation: From Simulation to Optimization,} George Corliss, Christ{\`e}le Faure, Andreas Griewank, Laurent Hasco{\"e}t, and Uwe Naumann (eds.), Springer, New York, 2001~\cite{Corliss2001b}. Authors compiled bibliographies for their own chapters. The separate bibliographies were merged into a single BibTex database. Because it includes all of the works cited by any chapter in this book, it includes most widely cited AD work and many citations that are not directly related to AD. For example, it includes basic references in optimization, symbolic algebra systems, and several applications areas.", comment = "", keywords = "", referred = "", isbn = "" } @BOOK{Corliss2001b, editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", note = "", publisher = "Springer", address = "New York", key = "Corliss2001b", abstract = "", comment = "", keywords = "", referred = "", isbn = "" } @TECHREPORT{Creusillet1996a, author = "Beatrice Creusillet and F. Irigoin", month = "January", year = 1996, title = "Interprocedural Array Region Analysis", number = "", note = "", address = "", institution = "A-282, Ecole des Mines de Paris, FRANCE", key = "Creusillet1996a", type = "Rapport CRI", abstract = "", comment = "", keywords = "", referred = "[Giering2001a]." } @ARTICLE{Csendes1997a, author = "Tibor Csendes and Dietmar Ratz", month = "", year = 1997, title = "Subdivision Direction Selection in Interval Methods for Global Optimization", journal = "SIAM J. Numer. Anal.", volume = 34, number = 3, pages = "922--938", note = "", key = "Csendes1997a", abstract = "", comment = "", keywords = "", referred = "[Kearfott2001a]." } @ARTICLE{Curtis1974a, author = "A. R. Curtis and Michael J. D. Powell and John K. Reid", month = "", year = 1974, title = "On the Estimation of Sparse {J}acobian Matrices", journal = "J. Inst. Math. Appl.", volume = 13, number = "", pages = "117--119", key = "Curtis1974a", abstract = "", comment = "", keywords = "", referred = "[Coleman1996a], [Geitner1996a], [Hossain2001a], [Griewank2001a]." } @ARTICLE{Dayde2000a, author = "Michel J. Dayde and Iain S. Duff", month = "", year = 2000, title = "The {RISC BLAS}: A Blocked Implementation of Level 3 {BLAS} for {RISC} Processors", journal = "ACM Trans. Math. Software", volume = 25, number = 3, pages = "316--340", note = "", key = "Dayde2000a", abstract = "", comment = "", keywords = "", referred = "[Aubert2001a]." } @ARTICLE{deJager1995a, author = "Bram {de~Jager}", year = 1995, title = "The Use of Symbolic Computation in Nonlinear Control: {I}s It Viable?", journal = "IEEE Trans. on Automatic Control", volume = "AC-40", number = 1, pages = "84--89", key = "deJager1995a", abstract = "", comment = "", keywords = "", referred = "[R{\"o}benack2001a]." } @ARTICLE{Dekker1971a, author = "Theodorus J. Dekker", month = "", year = 1971, title = "A Floating-Point Technique for Extending the Available Precision", journal = "Numer. Math.", volume = 18, number = "", pages = "224--242", note = "", key = "Dekker1971a", abstract = "", comment = "", keywords = "", referred = "[Braconnier2001a]." } @INPROCEEDINGS{Denk1999a, author = "Denk and U.~Feldmann and C.~{Hammer et al.}", editor = "", year = 1999, title = "Erweiterung eines {S}tandard-{S}chaltungs {S}imulators in {R}ichtung {VDHL-AMS}", booktitle = "Proceedings of ITG Workshop Analog '99, M{\"u}nchen", pages = "", publisher = "", address = "", key = "Denk1999a", abstract = "", comment = "", keywords = "", referred = "[Klein2001a]." } @BOOK{Dennis1996a, author = "John E. Dennis and Robert B. Schnabel", editor = "", year = 1996, title = "Numerical Methods for Unconstrained Optimization and Non-Linear Equations", series = "Classics in Applied Mathematics", number = 16, note = "", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Dennis1996a", abstract = "", comment = "", keywords = "", referred = "[Cappelaere2001a].", isbn = "0--89871--364--1" } @INCOLLECTION{Dignath2001a, author = "Florian Dignath and Peter Eberhard and Axel Fritz", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Analytical Aspects and Practical Pitfalls in Technical Applications of {AD}", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 14, pages = "131--136", note = "", publisher = "Springer", address = "New York", key = "Dignath2001a", crossref = "Corliss2001b", abstract = "We apply AD to three technical problems from multibody dynamics, vehicle dynamics and finite element material modeling. The multibody dynamics application investigates threshold and maximum-value optimization criteria in direct representation using AD for the sensitivity analysis. Secondly, an adaptive cruise controller of a vehicle convoy is optimized with respect to control error and control effort. Two experimental cars equipped with state-of-the-art sensors and actuators are used to verify the designed controllers. Since the engine voltage of the actuator is restricted to $\pm 10$ V, there are non-differentiable points in the time trajectory, but AD techniques can still be used. Thirdly, AD is used for the evaluation of constitutive relations for hyperelastic materials. Some important continuum mechanical quantities correspond to the first and second derivatives of the scalar stored energy function with respect to the strain tensor. These quantities can be derived analytically using complicated analysis but it is fascinating that with minimal preparation and only few mathematical insight exactly the same values can also be computed using AD methods.", comment = "", keywords = "", referred = "[Klein2001a].", isbn = "" } @PHDTHESIS{Dion1999a, author = "Claude Dion", month = "", year = 1999, title = "Dynamique de L'alignement et de L'orientation Moleculair{'e} Induite Par Laser. Simulations Num{\'e}riques sur {HCN} En Champ Infrarouge", note = "", address = "", school = "Universit\'e de Sherbrooke et Universit\'e de Paris-Sud", key = "Dion1999a", abstract = "", comment = "", keywords = "", referred = "[Ben-Haj-Yedder2001a]." } @INCOLLECTION{Dixon1991a, author = "Laurence C.~W.~Dixon", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "Use of Automatic Differentiation for Calculating {H}essians and {N}ewton Steps", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "114--125", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Dixon1991a", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "[Bischof1996b], [Gay1996a], [Mor\'e2001a], [Rall1996a].", isbn = "0--89871--284--X" } @ARTICLE{Dixon1991b, author = "Laurence C. W. Dixon", month = "", year = 1991, title = "On the Impact of Automatic Differentiation on the Relative Performance of Parallel Truncated {N}ewton and Variable Metric Algorithms", journal = "SIAM J. Optim.", volume = 1, number = "", pages = "475--486", note = "", key = "Dixon1991b", abstract = "", comment = "", keywords = "", referred = "[Mor\'e2001a]." } @TECHREPORT{Doherty1998a, author = "John J. Doherty", month = "September", year = 1998, title = "Strategy for Design Optimisation", number = "DERA/MSS5/CR980389/1.0", note = "", address = "", institution = "Defence Evaluation \& Research Agency", key = "Doherty1998a", type = "Customer Report", abstract = "", comment = "", keywords = "", referred = "[Forth2001a]." } @TECHREPORT{Dolan2000a, author = "Elizabeth D. Dolan and Jorge J. Mor{\'e}", month = "", year = 2000, title = "Benchmarking Optimization Software with {COPS}", number = "ANL/MCS-TM-246", note = "", address = "Argonne, Ill.", institution = "Argonne National Laboratory", key = "Dolan2000a", type = "Technical Memorandum", abstract = "", comment = "", keywords = "", referred = "[Mor\'e2001a]." } @BOOK{Dowd1998a, author = "Kevin Dowd and Charles R. Severence", editor = "", year = 1998, title = "High Performance Computing", series = "", number = "", note = "", publisher = "O'Reilly", address = "", key = "Dowd1998a", abstract = "", comment = "", keywords = "", referred = "[Bodin2001a].", isbn = "156592312X" } @BOOK{Draper1981a, author = "Norman R. Draper and Harry Smith", editor = "", year = 1981, title = "Applied Regression Analysis", edition = "second", series = "Wiley Series in Probability and Mathematical Statistics", number = "", note = "", publisher = "John Wiley and Sons, Inc.", address = "New York", key = "Draper1981a", abstract = "", comment = "See also 3rd edition (April 1998), John Wiley & Sons; ISBN: 0471170828", keywords = "", referred = "[Huiskes2001a].", isbn = "" } @TECHREPORT{Dryja1987a, author = "M. Dryja and O. B. Widlund", month = "", year = 1987, title = "An Additive Variant of the {S}chwarz Alternating Method for the Case of Many Subregions", number = 339, note = "", address = "New York", institution = "Department of Computer Science, Courant Institute", key = "Dryja1987a", type = "", abstract = "", comment = "", keywords = "", referred = "[Keyes2001a]." } @TECHREPORT{Duff1992a, author = "Iain~S. Duff and Roger~G. Grimes and John~G. Lewis", month = "", year = 1992, title = "Users' Guide for the {Harwell-Boeing} Sparse Matrix Collection ({Release I})", number = "tr/pa/92/86", note = "", address = "", institution = "CERFACS", key = "Duff1992a", type = "{T}echnical {R}eport", abstract = "", comment = "", keywords = "", referred = "[Hossain2001a]." } @ARTICLE{Duh1995a, author = "Der-Ming Duh and Anthony Douglas and John Haymet", month = "", year = 1995, title = "Integral Equation Theory for Uncharged Liquids: {T}he {L}ennard-{J}ones Fluid and the Bridge Function", journal = "J.~Chem.~Phys", volume = 103, number = "", pages = "2625-2633", note = "", key = "Duh1995a", abstract = "", comment = "", keywords = "", referred = "[Charpentier2001a]." } @ARTICLE{Dunn1989a, author = "J. C. Dunn and Dimitri P. Bertsekas", month = "", year = 1989, title = "Efficient Dynamic Programming Implementations of {N}ewton's Method for Unconstrained Optimal Control Problems", journal = "Journal of Optimization Theory and Applications", volume = 63, number = 1, pages = "23--38", key = "Dunn1989a", abstract = "", comment = "", keywords = "", referred = "[Christianson2001a]." } @PHDTHESIS{Dutschk1994a, author = "Roland Dutschk", month = "", year = 1994, title = "{G}eometrische {P}robleme bei {H}erstellung und {E}ingriff bogenverzahnter {K}egelr{\"a}der", note = "", address = "", school = "Technical University of Dresden", key = "Dutschk1994a", abstract = "", comment = "", keywords = "", referred = "[Vogel2001a]." } @INCOLLECTION{Eberhard1996a, author = "Peter Eberhard", editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank", year = 1996, title = "Adjoint Variable Method for the Sensitivity Analysis of Multibody Systems Interpreted as Continuous, Hybrid Form of Automatic Differentiation", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "319--328", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Eberhard1996a", crossref = "Berz1996c", abstract = "The multibody system approach is widely used for analyzing the dynamic behavior of mechanical systems with large motions, and several programs are available for this task. However, there is still a lack of tools for synthesizing nonlinear dynamic systems systematically by using optimization methods. Because the system's time behavior and optimization criteria can be computed only by numerical time integration, an analytical, closed form solution is not available for complicated, nonlinear multibody systems. Modern approaches such as the adjoint variable method offer the design engineer valuable tools to calculate required gradients for these problems in a reliable and efficient way. We show that the adjoint variable approach, developed from variational calculus is similar to automatic differentiation techniques, developed from recursive application of the chain rule. A parallel implementation of the adjoint variable approach yields further improvements in the computation time.", comment = "", keywords = "Multibody systems, mechanical systems, ordinary differential equations, adjoint variable method, parallel sensitivities.", referred = "[Dignath2001a]." } @ARTICLE{Eberhard1999a, author = "Peter Eberhard and Christian H.~Bischof", month = "", year = 1999, title = "Automatic Differentiation of Numerical Integration Algorithms", journal = "Mathematics of Computation", volume = 68, number = "", pages = "717--731", note = "", key = "Eberhard1999a", abstract = "", comment = "", keywords = "", referred = "[Dignath2001a], [Klein2001a], [Lee2001a]." } @BOOK{Eberhard2000a, author = "Peter Eberhard", editor = "", year = 2000, title = "Kontaktuntersuchungen an hybriden Mehr\-k{\"o}rper\-sys\-temen, Habilitation", series = "", number = "", note = "", publisher = "University of Stuttgart", address = "", key = "Eberhard2000a", abstract = "", comment = "", keywords = "", referred = "[Dignath2001a].", isbn = "" } @ARTICLE{Elliott1997a, author = "Jonathon Elliott and Jaime Peraire", month = "", year = 1997, title = "Practical 3{D} Aerodynamic Design and Optimization Using Unstructured Meshes", journal = "AIAA J.", volume = 35, number = 9, pages = "1479--1485", note = "", key = "Elliott1997a", abstract = "", comment = "", keywords = "", referred = "[Giles2001a]." } @INCOLLECTION{Evtushenko1991a, author = "Yuri G.~Evtushenko", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "Automatic Differentiation Viewed from Optimal Control", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "25--30", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Evtushenko1991a", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "[Chavent1996a], [Hoefkens2001a], [Irim91a], [Klein2001a], [Walther2001a].", isbn = "0--89871--284--X" } @ARTICLE{Evtushenko1997a, author = "Yuri G. Evtushenko and E. S. Zasuhina and V. I. Zubov", month = "", year = 1997, title = "Numerical Optimization of Solutions to {B}urgers' Problems by Means of Boundary Conditions", journal = "Computational Mathematics and Mathematical Physics", volume = 37, number = 12, pages = "1406--1414", note = "", key = "Evtushenko1997a", abstract = "", comment = "", keywords = "", referred = "[Evtushenko2001a]." } @ARTICLE{Evtushenko1998a, author = "Yuri G. Evtushenko", month = "", year = 1998, title = "Computation of Exact Gradients in Distributed Dynamic Systems", journal = "Optimization Methods and Software", volume = 9, number = "", pages = "45--75", note = "", key = "Evtushenko1998a", abstract = "", comment = "", keywords = "", referred = "[Caillau2001a], [Evtushenko2001a]." } @INCOLLECTION{Evtushenko2001a, author = "Yuri G.~Evtushenko and E.~S.~Zasuhina and V.~I.~Zubov", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "{FAD} Method to Compute Second Order Derivatives", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 39, pages = "327--333", note = "", publisher = "Springer", address = "New York", key = "Evtushenko2001a", crossref = "Corliss2001b", abstract = "We develop a unified methodology for computing second order derivatives of functions obtained in complex multistep processes and derive formulas for Hessians arising in discretization of optimal control problems. Where a process is described by continuous equations, we start with a discretization scheme for the state equations and derive exact gradient and Hessian expressions. We introduce adjoint systems for auxiliary vectors and matrices used for computing the derivatives. A unique discretization scheme is automatically generated for vector and matrix adjoint equations. The structure of the adjoint systems for some approximation schemes is found. The formulas for second derivatives are applied to examples.", comment = "", keywords = "", referred = "", isbn = "" } @INCOLLECTION{Faure1996a, author = "Christ{\`e}le Faure", editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank", year = 1996, title = "Splitting of Algebraic Expressions for Automatic Differentiation", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "117--127", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Faure1996a", crossref = "Berz1996c", abstract = "The number of products needed for the computation of a function and its first derivative is less than three times the number of essential products needed for the computation of the function itself, if each expression is split into binary subexpressions. We have implemented a split facility in Odyss\'ee to fit this theoretical idea. Odyss\'ee takes a set of subroutines as input and generates a new set of subroutines that compute the derivatives in forward or reverse mode. In practice, the decrease of the number of products does not lead to a decrease of run time, because current compilers do some sharing equivalent to a partial split and mismanage memory related to split variab", comment = "", keywords = "Complexity, split, algebraic expressions, Odyss\'ee", referred = "[Giles2001a]." } @TECHREPORT{Faure1998a, author = "Christ{\`e}le Faure and Yves Papegay", month = "September", year = 1998, title = "Odyss{\'e}e {U}ser's {G}uide. {V}ersion 1.7", number = "RT--0224", note = "See \url{www.inria.fr/RRRT/RT-0224.html}, and \url{www.inria.fr/safir/SAM/Odyssee/odyssee.html}.", address = "Sophia-Antipolis, France", institution = "INRIA", key = "Faure1998a", type = "Rapport technique", abstract = "", comment = "", keywords = "", referred = "[Ben-Haj-Yedder2001a], [Charpentier2001a], [Faure2001a], [Giles2001a], [Hascoet2001a], [Tijskens2001a]." } @TECHREPORT{Faure1999a, author = "Christ{\`e}le Faure and Patrick Dutto", month = "June", year = 1999, title = "Extension of {O}dyss{\'e}e to the {MPI} Library - {D}irect Mode", number = 3715, note = "", address = "", institution = "INRIA", key = "Faure1999a", type = "", abstract = "", comment = "", keywords = "", referred = "[Abate2001a], [Carle2001a]." } @TECHREPORT{Faure1999b, author = "Christ{\`e}le Faure and Isabelle Charpentier", month = "", year = 1999, title = "Comparing Automatically Generated and Hand Coded Adjoints", number = 3811, note = "", address = "", institution = "INRIA", key = "Faure1999a", type = "Rapport de recherche", abstract = "", comment = "", keywords = "", referred = "[Faure2001a]." } @TECHREPORT{Faure1999c, author = "Christ{\`e}le Faure and Patrick Dutto", month = "October", year = 1999, title = "Extension of {O}dyss{\'e}e to the {MPI} Library - {R}everse Mode", number = 3774, note = "", address = "", institution = "INRIA", key = "Faure1999c", type = "", abstract = "", comment = "", keywords = "", referred = "[Abate2001a], [Carle2001a]." } @TECHREPORT{Faure2000c, author = "Christ{\`e}le Faure and Edgar J. Souli{\'e} and Th{\'e}o Berclaz", month = "", year = 2000, title = "R{\'e}sonance paramagn{\'e}tique {\'e}lectronique, optimisation et diff{\'e}rentiation automatique", number = 3907, note = "", address = "", institution = "INRIA", key = "Faure2000c", type = "Rapport de recherche", abstract = "", comment = "", keywords = "", referred = "[Souli\'e2001a]." } @INCOLLECTION{Faure2001a, author = "Christ{\`e}le Faure and Uwe Naumann", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Minimizing the Tape Size", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 34, pages = "293--298", note = "", publisher = "Springer", address = "New York", key = "Faure2001a", crossref = "Corliss2001b", abstract = "For a real world program, most of the execution time of the adjoint code can be spend for the storage/retrieval of the tape recording operations for subsequent play-back. This execution time is proportional to the size of the tape. When writing adjoint code by hand, this is well known, and complex strategies are applied to limit the tape size. This paper is a first step towards the automatic control of the size of the tape.", comment = "", keywords = "", referred = "[Ben-Haj-Yedder2001a], [Giering2001a], [Hascoet2001a], [Klein2001a], [Naumann2001a].", isbn = "" } @ARTICLE{Faure2001b, author = "Christ{\`e}le Faure", month = "", year = "2001, in press", title = "Memory Limited Adjoint Code Generation", journal = "Flow, Turbulence and Combustion", volume = "", number = "", pages = "", note = "", key = "Faure2001b", abstract = "", comment = "", keywords = "", referred = "[Faure2001a]." } @ARTICLE{Faure2001c, author = "Christ{\`e}le Faure", month = "", year = 2001, title = "Adjoining Strategies for Multi-Layered Programs", journal = "{O}ptimisation {M}ethods and {S}oftware", volume = "", number = "", pages = "", note = "To appear. Also appeared as INRIA Rapport de recherche no. 3781, BP 105-78153 Le Chesnay Cedex, FRANCE, 1999.", key = "Faure2001c", abstract = "", comment = "", keywords = "", referred = "[Faure2001a], [Giering2001a]." } @INCOLLECTION{Feehery1996a, author = "William F.~Feehery and Paul I.~Barton", editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank", year = 1996, title = "A Differentiation-Based Approach to Dynamic Simulation and Optimization with High-Index Differential-Algebraic Equations", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "239--252", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Feehery1996a", crossref = "Berz1996c", abstract = "Reliable methods for solving simulation and dynamic optimization problems must be able to handle the high-index DAEs that arise naturally in these problems. This paper details a modified and automated version of the method of dummy derivatives for solving high-index DAEs that has been implemented within the ABACUSS large-scale equation based modeling environment. To implement our algorithm, we have developed a method for ``dummy variable pivoting'' into a standard DAE solver. Our approach requires a hybrid symbolic and numeric strategy in which we apply computational differentiation to the high-index system, and then employ a numerical integrator to solve the resulting index-1 system. We have modified the dummy derivative method for solving high-index DAEs in several ways to reduce the computational cost required to select and pivot the dummy derivative set. This work demonstrates the feasibility and desirability of using a hybrid numerical and symbolic strategy for the solution of certain classes of simulation and dynamic optimization problems.", comment = "", keywords = "Simulation, dynamic optimization, high-index DAEs, dummy derivatives, ABACUSS.", referred = "[Pusch1996a]." } @ARTICLE{Feehery1997a, author = "William F.~Feehery and John E.~Tolsma and Paul I.~Barton", month = "", year = 1997, title = "Efficient Sensitivity Analysis of Large-Scale Differential-Algebraic Equations", journal = "Appl.~Numer.~Math.", volume = 25, number = "", pages = "41--54", note = "", key = "Feehery1997a", abstract = "", comment = "", keywords = "", referred = "[Lee2001a]." } @TECHREPORT{Ferris1998a, author = "Michael C.~Ferris and Mike P. Mesnier and Jorge J.~Mor{\'e}", month = "", year = 1998, title = "{NEOS} and {Condor}: Solving Optimization Problems over the {Internet}", number = "ANL/MCS-P708-0398", note = "", address = "Argonne", institution = "Mathematics and Computer Science Division, Argonne National Laboratory", key = "Ferris1998a", type = "Preprint", abstract = "", keywords = "", referred = "[Lee2001a]." } @MASTERSTHESIS{Final2000a, author = "Mark Final", month = "", year = 2000, title = "Automatic Differentiation and Non-Linear Optimisation", note = "To appear", address = "College Lane, Hatfield, Herts AL10 9AB, UK", school = "University of Hertfordshire", key = "Final2000a", abstract = "", comment = "", keywords = "", referred = "[Casanova2001a]." } @INCOLLECTION{Fischer1991b, author = "Herbert Fischer", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "Special Problems in Automatic Differentiation", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "43--50", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Fischer1991b", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "[Bischof1996a], [Rall1996a].", isbn = "0--89871--284--X" } @INCOLLECTION{Flanders1991a, author = "Harley Flanders", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "Automatic Differentiation of Composite Functions", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "95--99", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Flanders1991a", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "[Rall1996a].", isbn = "0--89871--284--X" } @INCOLLECTION{Flanders2001a, author = "Harley Flanders", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Application of AD to a Family of Periodic Functions", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 38, pages = "319--326", note = "", publisher = "Springer", address = "New York", key = "Flanders2001a", crossref = "Corliss2001b", abstract = "We study the initial value problem (IVP) for the system $dx/dt=-y^{m}$, $dy/dt=x^{n}$, where $m$ and $n$ are positive odd integers, $x(0)=1$, $y(0)=0$. Its solutions are periodic, and we find relations between the periods. Automatic differentiation is used to enable interesting mathematical explorations.", comment = "", keywords = "", referred = "", isbn = "" } @ARTICLE{Fliess1995a, author = "Michel Fliess and Jean L{\'e}vine and Philippe Martin and Pierre Rouchon", year = 1995, title = "Flatness and Defect of Non-Linear Systems: {I}ntroductory Theory and Examples", journal = "Int. J. Control", volume = 61, number = "", pages = "1327--1361", key = "Fliess1995a", abstract = "", comment = "", keywords = "", referred = "[R{\"o}benack2001a]." } @BOOK{Ford1985a, author = "", editor = "Brian Ford and Fran{\c c}oise Chatelin", year = 1985, title = "Problem Solving Environments for Scientific Computing", series = "", number = "", note = "", publisher = "North Holland", address = "", key = "Ford1985a", abstract = "", comment = "", keywords = "", referred = "[Hague2001a].", isbn = "0 444 702547" } @TECHREPORT{Forth1998a, author = "Shaun A. Forth", month = "", year = 1998, title = "Automatic Differentiation for Flux Linearisation", number = "98/1", note = "Poster Presentation at {\em 16th International Conference on Numerical Methods in Fluid Dynamics}, July 6-10, 1998, Arcachon, France", address = "Swindon SN6 8LA, England", institution = "Cranfield University (RMCS Shrivenham)", key = "Forth1998a", type = "AMOR Report", abstract = "", comment = "", keywords = "", referred = "[Tadjouddine2001a]." } @INCOLLECTION{Forth2001a, author = "Shaun A.~Forth and Trevor P.~Evans", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Aerofoil Optimisation via AD of a Multigrid Cell-Vertex {E}uler Flow Solver", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 17, pages = "153--160", note = "", publisher = "Springer", address = "New York", key = "Forth2001a", crossref = "Corliss2001b", abstract = "We report preliminary results in the use of ADIFOR 2.0 to determine aerodynamic sensitivities of a 2-D airfoil with respect to geometrical variables. Meshes are produced with a hyperbolic interpolation technique. The flow field is calculated using the cell-vertex method of Hall, which incorporates local time-stepping, mesh sequencing and multigrid. We present results and timings using both Finite Differences (FD) and Automatic Differentiation (AD). We investigate the effect of starting the perturbed calculation for FD and the derivative calculation for AD from either the current or freestream conditions and highlight the need for careful implementation of convergence criteria. We attempt to make a comparative study of AD and FD gradients in an aerofoil optimisation, using the DERA CODAS method from the perspective of DERA's eventual aim, 3D viscous optimisation of wing-body configurations.", comment = "", keywords = "", referred = "[Cappelaere2001a], [Haase2001a], [Klein2001a]", isbn = "" } @ARTICLE{Fraser1999a, author = "D. A. S. Fraser", month = "", year = 1999, title = "Regression Analysis, Nonlinear or Nonnormal: {S}imple and Accurate p Values from Likelihood Analysis", journal = "Journal of the American Statistical Association", volume = 94, number = 448, pages = "1286--1295", note = "", key = "Fraser1999a", abstract = "", comment = "", keywords = "", referred = "[Huiskes2001a]." } @INPROCEEDINGS{Fritz1999a, author = "Axel Fritz", editor = "J. Ambrosio and W. Schiehlen", year = 1999, title = "Optimal Control of a Vehicle Convoy", booktitle = "Proceedings EUROMECH 404, Lissabon, Advances in Computational Multibody Dynamics", series = "", number = "", pages = "695--712", note = "", publisher = "", address = "", key = "Fritz1999a", abstract = "", comment = "", keywords = "", referred = "[Dignath2001a]." } @ARTICLE{Fulcheri1998a, author = "Pascale Fulcheri and Martine Olivi", month = "", year = 1998, title = "Matrix Rational {$H_2$} Approximation: {A} Gradient Algorithm Based on {S}chur Analysis", journal = "SIAM J. Cont. Optim.", volume = 36, number = 6, pages = "2103-2127", note = "", key = "Fulcheri1998a", abstract = "", comment = "", keywords = "", referred = "[Grimm2001a]." } @ARTICLE{F÷llinger1978a, author = "Otto F{\"o}llinger", year = 1978, title = "{E}ntwurf zeitvarianter {S}ysteme durch {P}olvorgabe", journal = "Regelungstechnik", volume = 26, number = 6, pages = "189--196", key = "F{\"o}llinger1978a", abstract = "", comment = "", keywords = "", referred = "[R{\"o}benack2001a]." } @MISC{GAMS2000a, author = "", month = "", year = "", title = "{GAMS}", note = "See \url{www.gams.com}", howpublished = "", key = "GAMS2000a", abstract = "", comment = "", keywords = "", referred = "" } @ARTICLE{Gan1992a, author = "Hin-Hark Gan and Byung Chan Eu", month = "", year = 1992, title = "{O}rnstein-{Z}ernike Derivative Relations and Thermodynamic Functions", journal = "J.~Chem.~Phys", volume = 96, number = "", pages = "558-564", note = "", key = "Gan1992a", abstract = "", comment = "", keywords = "", referred = "[Charpentier2001a]." } @INCOLLECTION{Garcia1991a, author = "Oscar Garc{\'{\i}}a", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "A System for the Differentiation of {F}ortran Code and an Application to Parameter Estimation in Forest Growth Models", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "273--286", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Garcia1991a", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "[Jued91a], [Soul91a].", isbn = "0--89871--284--X" } @INCOLLECTION{Gay1991a, author = "David M.~Gay", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "Automatic Differentiation of Nonlinear {AMPL} Models", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "61--73", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Gay1991a", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "[Gay1996a].", isbn = "0--89871--284--X" } @INCOLLECTION{Gay1996a, author = "David M.~Gay", editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank", year = 1996, title = "More {AD} of Nonlinear {AMPL} Models: {C}omputing {H}essian Information and Exploiting Partial Seperability", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "173--184", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Gay1996a", crossref = "Berz1996c", abstract = "We describe computational experience with automatic differentiation of mathematical programming problems expressed in the modeling language AMPL. Nonlinear expressions are translated to loop-free code, which makes it easy to compute gradients and Jacobians by backward automatic differentiation. The nonlinear expressions may be interpreted or, to gain some evaluation speed at the cost of increased preparation time, converted to Fortran or C. We have extended the interpretive scheme to evaluate Hessian (of Lagrangian) times vector. Detecting partially separable structure (sums of terms, each depending, perhaps after a linear transformation, on only a few variables) is of independent interest, as some solvers exploit this structure. It can be detected automatically by suitable ``tree walks''. Exploiting this structure permits an AD computation of the entire Hessian matrix by accumulating Hessian times vector computations for each term, and can lead to a much faster computation of the Hessian than by computing the whole Hessian times each unit vector.", comment = "", keywords = "AMPL, Hessian, partial separability, tree walks." } @INPROCEEDINGS{Geffroy1996a, author = "Sophie Geffroy and Richard Epenoy and Joseph Noailles", editor = "", year = 1996, title = "Averaging Techniques in Optimal Control for Orbital Low-Thrust Transfers and Rendez-vous Computation", booktitle = "Proceedings of the 11th International Astrodynamics Symposium", series = "", number = "", pages = "166--171", note = "", publisher = "", address = "Gifu, Japan", key = "Geffroy1996a", abstract = "", comment = "", keywords = "", referred = "[Caillau2001a]." } @INCOLLECTION{Geitner1996a, author = "Uwe Geitner and Jean Utke and Andreas Griewank", editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank", year = 1996, title = "Automatic Computation of Sparse {J}acobians by Applying the Method of {N}ewsam and {R}amsdell", booktitle = "Computational Differentiation: Techniques Applications, and Tools", pages = "161--172", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Geitner1996a", crossref = "Berz1996c", abstract = "The computation of sparse Jacobians is a common subproblem in iterative numerical algorithms. The sparsity structure is not always known a priori and may sometimes change from point to point. The subject of this paper is the automatic detection of the sparsity structure and its exploitation for an efficient computation of Jacobians using automatic differentiation, graph coloring, and fast solution algorithms for Vandermonde systems.", comment = "", keywords = "Sparse Jacobians, graph coloring, Newsam-Ramsdell, Vandermonde systems.", referred = "[Griewank2001a], [Hossain2001a]." } @TECHREPORT{Gertz2000a, author = "E. Michael Gertz and Philip E. Gill and Julia Muetherig", month = "", year = 2000, title = "User's Guide for {SnadiOpt}: A Package Adding Automatic Differentiation to {Snopt}", number = "NA 01--1", note = "", address = "San Diego", howpublished = "", institution = "Department of Mathematics, University of California", key = "Gertz2000a", type = "Report", abstract = "", comment = "", keywords = "", referred = "[Abate2001a], [Lee2001a]." } @MANUAL{Giering1997a, author = "Ralf Giering", month = "December", year = 1997, title = "{T}angent Linear and {A}djoint {M}odel {C}ompiler, Users Manual", number = "", note = "Unpublished. Available at \url{puddle.mit.edu/~ralf/tamc}.", address = "Cambridge, MA", institution = "Center for Global Change Sciences, Department of Earth, Atmospheric, and Planetary Science, MIT", organization = "Center for Global Change Sciences, Department of Earth, Atmospheric, and Planetary Science, MIT", key = "Giering1997a", type = "", abstract = "", comment = "", keywords = "", referred = "[Giering2001a], [Gockenbach2001a], [Hascoet2001a], [Souli2001a], [Tadjouddine2001a]." } @ARTICLE{Giering1998a, author = "Ralf Giering and Thomas Kaminski", month = "", year = 1998, title = "Recipies for Adjoint Code Construction", journal = "ACM Trans. Math. Software", volume = 24, number = 4, pages = "437--474", note = "Also appeared as Max-Planck Institut f{\"u}r Meteorologie Hamburg, Technical Report No. 212, 1996.", key = "Giering1998a", abstract = "", comment = "", keywords = "", referred = "[Giering2001a], [Giles2001a], [Kim2001a], [Klein2001a]." } @TECHREPORT{Giering2000b, author = "Ralf Giering and Thomas Kaminski", month = "", year = 2000, title = "On the Performance of Derivative Code Generated by {TAMC}", number = "", note = "Submitted to Optimization Methods and Software. See \url{www.FastOpt.de/papers/perftamc.ps.gz}.", address = "Hamburg, Germany", institution = "FastOpt", key = "Giering2000b", type = "Manuscript", abstract = "", comment = "", keywords = "", referred = "[Giering2001a], [Mor\'e2001a]." } @INCOLLECTION{Giering2001a, author = "Ralf Giering and Thomas Kaminski", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Generating Recomputations in Reverse Mode {AD}", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 33, pages = "283--291", note = "", publisher = "Springer", address = "New York", key = "Giering2001a", crossref = "Corliss2001b", abstract = "The main challenge of the reverse (or adjoint) mode of automatic differentiation (AD) is providing the accurate values of required variables to the derivative code. We discuss different strategies to tackle this challenge. The ability to generate efficient adjoint code is crucial for handling large scale applications. For challenging applications, efficient adjoint code must provide at least a fraction of the values of required variables through recomputations, but it is essential to avoid unnecessary recomputations. This is achieved by the Efficient Recomputation Algorithm implemented in the Tangent linear and Adjoint Model Compiler and in Transformation of Algorithms in Fortran, which are source-to-source translation AD tools for Fortran programs. We describe the algorithm and discuss possible improvements.", comment = "", keywords = "", referred = "[Faure2001a], [Griewank2001a], [Klein2001a].", isbn = "" } @TECHREPORT{Gilbert1991a, author = "Jean-Charles Gilbert and Georges {Le Vey} and John Masse", year = 1991, title = "La Diff\'erentiation Automatique de Fonctions Repr\'esent\'ees par des Programmes", number = 1557, pages = "", address = "Le Chesnay, France", institution = "INRIA", key = "Gilbert1991a", type = "Rapport de Recherche", abstract = "", comment = "", keywords = "", referred = "[Cappelaere2001a], [Hassold1996a]." } @TECHREPORT{Gilbert1995a, author = "Jean-Charles Gilbert and Claude Lemar{\'e}chal", month = "", year = 1995, title = "The Modules {M1QN3} and {N1QN3}. {V}ersion 2.0c.", number = "", note = "", address = "", institution = "INRIA", key = "Gilbert1995a", type = "", abstract = "", comment = "", keywords = "", referred = "[Cappelaere2001a]." } @TECHREPORT{Giles2000a, author = "Michael B. Giles", month = "", year = 2000, title = "On the Use of {R}unge-{K}utta Time-Marching and Multigrid for the Solution of Steady Adjoint Equations", number = "NA00/10", note = "", address = "", institution = "Oxford University Computing Laboratory", key = "Giles2000a", type = "{T}echnical {R}eport", abstract = "", comment = "", keywords = "", referred = "[Giles2001a]." } @INCOLLECTION{Giles2001a, author = "Michael B. Giles", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "On the Iterative Solution of Adjoint Equations", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 16, pages = "145--151", note = "", publisher = "Springer", address = "New York", key = "Giles2001a", crossref = "Corliss2001b", abstract = "This paper considers the iterative solution of the adjoint equations which arise in the context of design optimisation. It is shown that naive adjoining of the iterative solution of the original linearised equations results in an adjoint code which cannot be interpreted as an iterative solution of the adjoint equations. However, this can be achieved through appropriate algebraic manipulations. This is important in design optimisation because one can reduce the computational cost by starting the adjoint iteration from the adjoint solution obtained in the previous design step.", comment = "", keywords = "", referred = "[Klein2001a]", isbn = "" } @ARTICLE{Giles2001b, author = "Michael B. Giles and Niles A. Pierce", month = "", year = "to appear", title = "An Introduction to the Adjoint Approach to Design", journal = "Flow, Turbulence and Combustion", volume = "", number = "", pages = "", key = "Giles2001b", abstract = "", comment = "", keywords = "", referred = "[Giles2001a]." } @ARTICLE{Gill1978a, author = "Philip E.~Gill and Walter Murray", month = "", year = 1978, title = "Algorithms for the Solution of the Nonlinear Least-Squares Problem", journal = "SIAM J. Numer. Anal.", volume = 15, number = 5, pages = "977--992", note = "", key = "Gill1978a", abstract = "", comment = "", keywords = "", referred = "[Bischof2001a]." } @BOOK{Gill1981a, author = "Philip E. Gill and Walter Murray and Margret H. Wright", year = 1981, title = "Practical Optimization", series = "", number = "", publisher = "Academic Press", address = "New York", key = "Gill1981a", abstract = "", comment = "", keywords = "", referred = "[Chavent1996a], [Giles2001a], [Haase2001a], [Huiskes2001a], [Kubota1996a].", isbn = "" } @TECHREPORT{Gill1997a, author = "Philip E.~Gill and Walter Murray and Michael A.~Saunders", month = "", year = 1997, title = "{SNOPT}: An {SQP} Algorithm for Large-Scale Constrained Optimisation", number = "97-2", note = "", address = "San Diego, La Jolla, CA", institution = "Department of Mathematics, University of California", key = "Gill1997a", type = "Numerical Analysis Report", abstract = "", comment = "", keywords = "", referred = "[Casanova2001a]." } @ARTICLE{Gockenbach1999a, author = "Mark S. Gockenbach and M. J. Petro and William W. Symes", month = "", year = 1999, title = "C++ Classes for Linking Optimization with Complex Simulations", journal = "ACM Trans. Math. Software", volume = 25, number = 2, pages = "191--212", note = "", key = "Gockenbach1999a", abstract = "", comment = "", keywords = "", referred = "[Gockenbach2001a]." } @ARTICLE{Gockenbach2000a, author = "Mark S. Gockenbach and Daniel R. Reynolds and William W. Symes", month = "", year = "submitted", title = "Efficient and Automatic Implementation of the Adjoint State Method", journal = "ACM Trans. Math. Software", volume = "", number = "", pages = "", key = "Gockenbach2000a", abstract = "", comment = "", keywords = "", referred = "[Gockenbach2001a]." } @TECHREPORT{Gockenbach2000b, author = "Mark S. Gockenbach", month = "", year = 2000, title = "Understanding Code Generated by {TAMC}", number = "00-30", note = "", address = "Houston, Texas, U.S.A", institution = "Department of Computational and Applied Mathematics, Rice University", key = "Gockenbach2000b", type = "{T}echnical {R}eport", abstract = "", comment = "", keywords = "", referred = "[Gockenbach2001a]." } @INCOLLECTION{Gockenbach2001a, author = "Mark S.~Gockenbach and Daniel R.~Reynolds and William W.~Symes", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Automatic Differentiation and the Adjoint State Method", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 18, pages = "161--166", note = "", publisher = "Springer", address = "New York", key = "Gockenbach2001a", crossref = "Corliss2001b", abstract = "The C++ class {\tt fdtd} uses automatic differentiation techniques to implement an abstract time stepping scheme in an object-oriented fashion, making it possible to use the resulting simulator to solve inverse or control problems. The class takes a complete specification of a {\em single step} of the scheme, and assembles from it a complete simulator, along with the linearized and adjoint simulations. The result is a (nonlinear) operator in the sense of the Hilbert Class Library, a C++ package for optimization. Performance is equivalent to that of optimized Fortran implementations.", comment = "", keywords = "", referred = "", isbn = "" } @ARTICLE{Goldfarb1984a, author = "Donald Goldfarb and Philippe L.~Toint", month = "", year = 1984, title = "Optimal Estimation of {J}acobian and {H}essian Matrices That Arise in Finite Difference Calculations", journal = "Mathematics of Computation", volume = 43, number = 167, pages = "69--88", note = "", key = "Goldfarb1984a", abstract = "", comment = "", keywords = "", referred = "[Abate2001a], [Hossain2001a]." } @INCOLLECTION{Goldman1991a, author = "Victor V.~Goldman and J.~Molenkamp and J.~A.~{van Hulzen}", editor = "Andreas Griewank and George F. Corliss", year = 1991, title = "Efficient Numerical Program Generation and Computer Algebra Environments", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "74--83", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Goldman1991a", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "[Bischof1996b], [Char91a], [Garc91a], [Goldman1996a], [Monagan1996a]." } @INCOLLECTION{Goldman1996a, author = "Victor V. Goldman and Gerard Cats", editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank", year = 1996, title = "Automatic Adjoint Modelling within a Program Generation Framework: {A} Case Study for a Weather Forecasting Grid-Point Model", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "185--194", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Goldman1996a", crossref = "Berz1996c", abstract = "A specification-based method for the automatic generation of executable Fortran adjoint code is presented. The method is embedded within the program generation framework for the forward model, and automatic differentiation techniques are applied to the forward-model specifications themselves rather than to its Fortran source. A distinction is made between linearization and stencil processing. For the latter, special adjointing rules for stencil operators are used. The work is discussed in the light of various computational differentiation issues including arithmetic efficiency, forward/reverse hybridization trade-offs, portability to high-performance platforms, and source-to-source adjoint methodologies. Results of a computer algebra-based prototype are illustrated for forward and adjoint code for the dynamics part of a high-resolution, limited-area weather forecasting grid-point model.", comment = "", keywords = "Specification-based methods, high-level Jacobian representations, stencil operator adjoint, boundary conditions, Fortran 90, HIRLAM.", referred = "[Chavent1996a]." } @BOOK{Goursat1904a, author = "{\'E}douard Goursat and Earle R. Hedrick", editor = "", year = 1904, title = "A Course in Mathematical Analysis I", series = "", number = "", note = "", publisher = "Ginn", address = "", key = "Goursat1904a", abstract = "", comment = "", keywords = "", referred = "[Flanders2001a].", isbn = "" } @TECHREPORT{Grachev1986a, author = "N. I. Grachev and A. N. Filkov", month = "", year = 1986, title = "Solution of Optimal Control Problems in System {DISO}", number = "", note = "(In Russian)", address = "Moscow", institution = "Computing Center of Russian Academy of Sciencesy", key = "Grachev1986a", type = "", abstract = "", comment = "", keywords = "", referred = "[Evtushenko2001a]." } @INCOLLECTION{Griewank1982a, author = "Andreas Griewank and Philippe L. Toint", editor = "Michael J.~D.~Powell", year = 1982, title = "On the Unconstrained Optimization of Partially Separable Functions", booktitle = "Nonlinear Optimization 1981", volume = "", pages = "301--312", publisher = "Academic Press", address = "New York", key = "Griewank1982a", abstract = "", comment = "", keywords = "", referred = "[Gay1996a], [Klein2001a], [Mor\'e2001a]." } @INCOLLECTION{Griewank1989a, author = "Andreas Griewank", editor = "Masao Iri and Kunio Tanabe", year = 1989, title = "On Automatic Differentiation", booktitle = "Mathematical Programming: Recent Developments and Applications", pages = "83--108", publisher = "Kluwer Academic Publishers", address = "Dordrecht", key = "Griewank1989a", abstract = "", comment = "Also appeared as Preprint MCS--P10--1088, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill., October 1988.", keywords = "", referred = "[Abate2001a], [Bischof1996b], [Cappelaere2001a], [Carle1996a], [Christianson1996a], [Giering1997a], [Giering2001a], [Hutschenreiter1996a], [Kim2001a], [Rall1996a], [Tijskens2001a].", isbn = "079230490X" } @ARTICLE{Griewank1989b, author = "Andreas Griewank and George W.~Reddien", month = "", year = 1989, title = "Computation of Cusp Singularities for Operator Equations and Their Discretizations", journal = "Journal of Computational and Applied Mathematics", volume = "", number = "", pages = "133--153", key = "Griewank1989b", abstract = "", comment = "", keywords = "", referred = "[Hutschenreiter1996a], [Vogel2001a]." } @ARTICLE{Griewank1991a, author = "Andreas Griewank", month = "", year = 1991, title = "The Chain Rule Revisited in Scientific Computing", journal = "SIAM News", volume = 24, number = "", pages = "", note = "no. 3, p. 20 \& no. 4, p. 8", key = "Griewank1991a", abstract = "", keywords = "", referred = "[Rall1996a]." } @INCOLLECTION{Griewank1991c, author = "Andreas Griewank and Shawn Reese", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "On the Calculation of {J}acobian Matrices by the {M}arkowitz Rule", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "126--135", note = "", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Griewank1991c", crossref = "Griewank1991e", abstract = "", comment = "Also appeared as Preprint MCS--P267--1091, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill., January 1992.", keywords = "", referred = "[Bischof1996b], [Corl91a]; [Feehery1996a], [Irim91a], [Naumann2001a], [Tadjouddine2001a].", isbn = "0--89871--284--X" } @INCOLLECTION{Griewank1991d, author = "Andreas Griewank", editor = "R. Seydel and F. W. Schneider and T. K{\"u}pper and H. Troger", month = "", year = 1991, title = "Automatic Evaluation of First- and Higher-Derivative Vectors", booktitle = "Proceedings of the Conference at W{\"u}rzburg, Aug. 1990, Bifurcation and Chaos: {A}nalysis, Algorithms, Applications", volume = 97, chapter = "", pages = "135--148", publisher = "Birkh{\"a}user Verlag", address = "Basel, Switzerland", key = "Griewank1991d", abstract = "", comment = "", keywords = "", referred = "[Bisc1991a], [Beley2001a]." } @BOOK{Griewank1991e, editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Griewank1991e", abstract = "", comment = "Proceedings of the SIAM Workshop on the Automatic Differentiation of Algorithms in Breckenridge, Colorado, January 6 -- 8, 1991.", keywords = "", referred = "[Fuchi1996a], [Geitner1996a], [Goldman1996a], [Hutschenreiter1996a], [Klein2001a], [Kubota1996a], [Rall1996a].", isbn = "0--89871--284--X" } @ARTICLE{Griewank1992a, author = "Andreas Griewank", month = "", year = 1992, title = "Achieving Logarithmic Growth of Temporal and Spatial Complexity in Reverse Automatic Differentiation", journal = "Optimization Methods and Software", volume = 1, number = "", pages = "35--54", note = "", key = "Griewank1992b", abstract = "", comment = "Also appeared as Preprint MCS--P228--0491, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill., April 1991.", keywords = "", referred = "[Benary1996a], [Christianson2001a], [Giering1997a], [Giering2001a], [Gockenbach2001a], [Goldman1996a], [Grimm1996a], [Hascoet2001a], [Klein2001a], [Mohammadi1996a], [Rall1996a], [Souli2001a], [Walter2001a]." } @INPROCEEDINGS{Griewank1994a, author = "Andreas Griewank", year = 1994, title = "Automatic Directional Differentiation of Nonsmooth Composite Functions", booktitle = "Recent Developments in Optimization, French-German Conference on Optimization", pages = "", publisher = "", address = "Dijon", key = "Griewank1994a", abstract = "", comment = "", keywords = "", referred = "[Berz2001a], [Hassold1996a]." } @ARTICLE{Griewank1996b, author = "Andreas Griewank and David Juedes and Jean Utke", month = "", year = 1996, title = "{ADOL--C}, A Package for the Automatic Differentiation of Algorithms Written in {C/C++}", journal = "ACM Trans. Math. Software", volume = 22, number = 2, pages = "131--167", note = "See \url{ftp://info.mcs.anl.gov/pub/tech_reports/reports/TM162.ps}", key = "Griewank1996b", abstract = "", comment = "Also appeared as Preprint MCS--P180--1190, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill., November 1990.", keywords = "", referred = "[Aubert2001a], [Beley2001a], [Benary1996a], [Bischof1996b], [Juedes1996a], [Kearfott1996a], [Klein1996a], [Klein2001a], [Gay1996a], [Geitner1996a], [Griewank2001a], [Guckenheimer1996a], [Haase2001a], [Huiskes2001a], [Hutschenreiter1996a], [Monagan1996a], [Mor\'e2001a], [Rall1996a], [R{\"o}benack2001a], [Shiriaev1996a], [Utke1996a]." } @TECHREPORT{Griewank1996c, author = "Andreas Griewank and David Juedes and Jean Utke", month = "", year = 1996, title = "A Package for the Automatic Differentiation of Algorithms Written in {C/C++}. {U}ser Manual", number = "", note = "See \url{www.math.tu-dresden.de/wir/project/wwwadolc/index.html}.", address = "Dresden, Germany", institution = "Institute of Scientific Computing, Technical University of Dresden", key = "Griewank1996c", type = "", abstract = "", comment = "", keywords = "", referred = "[Tijskens2001a]." } @INCOLLECTION{Griewank1997a, author = "Andreas Griewank and George F. Corliss and Petra Henneberger and Gabriella Kirlinger and Florian A. Potra and Hans J. Stetter", editor = "", year = 1997, title = "High-Order Stiff {ODE} Solvers via Automatic Differentiation and Rational Prediction", booktitle = "Numerical Analysis and Its Applications", series = "Lecture Notes in Computer Science", number = 1196, pages = "114--125", note = "Also appeared as Technical Report IOKOMO 02 96, Technical University of Dresden", publisher = "Springer", address = "Berlin", key = "Griewank1997a", abstract = "", comment = "", keywords = "", referred = "[Beley2001a]." } @TECHREPORT{Griewank1999a, author = "Andreas Griewank and David Juedes and H.~Mitev and Jean Utke and Olaf Vogel and Andrea Walther", month = "", year = 1999, title = "{ADOL-C}: {A} Package for the Automatic Differentiation of Algorithms Written in {C/C++}", number = "", note = "Updated version of the paper published in {\it ACM Trans. Math. Software} 22, 1996, 131--167", address = "", institution = "Technical University of Dresden, Institute of Scientific Computing and Institute of Geometry", key = "Griewank1999a", type = "", abstract = "", comment = "", keywords = "", referred = "[Vogel2001a]." } @ARTICLE{Griewank1999b, author = "Andreas Griewank and Andrea Walther", month = "", year = 1999, title = "Algorithm 799: {R}evolve: {A}n Implementation of Checkpoint for the Reverse or Adjoint Mode of Computational Differentiation", journal = "ACM Trans. Math. Software", volume = 26, number = 1, pages = 19, note = "Also appeared as Technical University of Dresden, Technical Report IOKOMO-04-1997.", key = "Griewank1999b", abstract = "", comment = "", keywords = "", referred = "[Christianson2001a]." } @BOOK{Griewank2000a, author = "Andreas Griewank", editor = "", year = 2000, title = "Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation", booktitle = "", series = "Frontiers in Appl. Math.", number = 19, note = "", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Griewank2000a", abstract = "", comment = "", keywords = "", referred = "[Abate2001a], [Beley2001a], [Cappelaere2001a], [Dignath2001a], [Faure2001a], [Forth2001a], [Giering2001a], [Haase2001a], [Hascoet2001a], [Kim2001a], [Klein2001a], [Mor\'e2001a], [R{\"o}benack2001a], [Souli\'e2001a], [Tadjouddine2001a], [Tijskens2001a].", isbn = "0--89871--451--6" } @ARTICLE{Griewank2000b, author = "Andreas Griewank and Jean Utke and Andrea Walther", month = "", year = 2000, title = "Evaluating Higher Derivative Tensors by Forward Propagation of Univariate {T}aylor Series", journal = "Mathematics of Computation", volume = 69, number = "", pages = "1117--1130", note = "", key = "Griewank2000b", abstract = "", comment = "", keywords = "", referred = "[Klein2001a], [Vogel2001a]." } @TECHREPORT{Griewank2000c, author = "Andreas Griewank and Christo Mitev", month = "", year = 2000, title = "Detecting {J}acobian Sparsity Patterns by {B}ayesian Probing", number = "IOKOMO-04-2000", note = "Submitted to Math.~Progr.", address = "", institution = "Technical University of Dresden", key = "Griewank2000c", type = "Preprint", abstract = "", comment = "", keywords = "", referred = "[Griewank2001a]." } @MISC{Griewank2000e, author = "Andreas Griewank", month = "", year = 2000, title = "", note = "", howpublished = "{P}rivate communication", key = "Griewank2000e", abstract = "", comment = "", keywords = "", referred = "[Berz2001a]." } @INCOLLECTION{Griewank2001a, author = "Andreas Griewank and Christo Mitev", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Verifying Jacobian Sparsity", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 32, pages = "271--279", note = "", publisher = "Springer", address = "New York", key = "Griewank2001a", crossref = "Corliss2001b", abstract = "In a recent paper~\cite{Griewank2000c} we describe an automatic procedure for successively reducing the set of possible nonzeros in a Jacobian matrix until eventually the exact sparsity pattern is obtained. The dependence information needed in this probing process consists of ``Boolean products'' Jacobian-vector products and vector-Jacobian products, which can be evaluated by propagating Boolean variables forward or backward through the function evaluation procedure. Starting from a user specified (or by default initialized) prior probability distribution, the procedure suggests a sequence of probing vectors. The resulting information is then used according to Bayes' law to update the probabilities that certain elements are nonzero. We analyze the special situation where the sparsity pattern is provided as a guess and merely needs to be verified with a small number of probes. For banded $n \times n$ matrices with $h$ superdiagonals it is shown that the greedy heuristics developed in~\cite{Griewank2000c} requires in verification mode only $O(h +\log_2 n)$ probes. Our numerical results indicate that this is still true if nothing is known a priori about the sparsity pattern.", comment = "", keywords = "", referred = "", isbn = "" } @INCOLLECTION{Griffith1996a, author = "Anne K.~Griffith and Nancy K.~Nichols", editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank", year = 1996, title = "Accounting for Model Error in Data Assimilation Using Adjoint Models", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "195--204", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Griffith1996a", crossref = "Berz1996c", abstract = "We consider a modification to the variational assimilation method, in which a correction term is added to the model equations. This correction term is determined in the assimilation procedure and produces a solution that is closer to the observed data and compensates to some extent for model error. The 1-D shallow water equations are used to illustrate the variational assimilation method, with and without the correction term, in the presence of model error.", comment = "", keywords = "Data assimilation, adjoint model, model error, control variable.", referred = "" } @MASTERSTHESIS{Griffiths1992a, author = "R.~Griffiths", month = "", year = 1992, title = "Minimum Lap Time Simulation of a Racing Car", note = "", address = "", school = "School of Mechanical Engineering, Cranfield University", key = "Griffiths1992a", abstract = "", comment = "", keywords = "", referred = "[Casanova2001a]." } @INCOLLECTION{Grimm1996a, author = "Jos{\'e} Grimm and Lo{\"{\i}}c Pottier and Nicole Rostaing-Schmidt", editor = "Martin Berz and Christian H.~Bischof and George F.~Corliss and Andreas Griewank", year = 1996, title = "Optimal Time and Minimum Space-Time Product for Reversing a Certain Class of Programs", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "95--106", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Grimm1996a", crossref = "Berz1996c", abstract = "This paper concerns space-time trade-offs for the reverse mode of automatic differentiation on the straight-line programs with nested loops. In the first part we consider the problem of reversing a finite sequence given by $u_{n+1}=f(u_{n})$, which can model a certain class of finite loops. We show an optimal time strategy for this problem, the number of available registers being fixed, and a lower bound on the space-time product equal to $\frac{p (\ln p)^{2}}{(\ln 4)^{2}}$. We then present an optimal strategy on nested loops with the objective of preserving the program structure. Finally, we consider an application of this storage/recomputation strategy to compute in reverse mode the derivatives of a function represented as a Fortran program.", comment = "", keywords = "Space-time trade-off, optimal time strategy, nested loops, lower bound on space-time product, Odyss\'ee.", referred = "[Klein2001a], [Mohammadi1996a], [Souli\'e2001a]." } @TECHREPORT{Grimm2000a, author = "Jos{\'e} Grimm", month = "September", year = 2000, title = "Rational Approximation of Transfer Functions in the Hyperion Software", number = 4002, note = "", address = "", institution = "INRIA", key = "Grimm2000a", type = "Rapport de recherche", abstract = "", comment = "", keywords = "", referred = "[Grimm2001a]." } @INCOLLECTION{Grimm2001a, author = "Jos{\'e} Grimm", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Complexity Analysis of Automatic Differentiation in the Hyperion Software", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 36, pages = "305--310", note = "", publisher = "Springer", address = "New York", key = "Grimm2001a", crossref = "Corliss2001b", abstract = "One important feature of the hyperion software is the rational approximation problem: given the $m$ first terms of the power series expansion of a stable transfer function, find a stable approximation of it under the form $P/q$, of McMillan degree $n$. This leads to minimising $\psi(Q)$, for some $Q$. In this chapter, we show different ways of computing $\psi$ and its derivatives, and we indicate the complexity of these computations.", comment = "", keywords = "", referred = "", isbn = "" } @BOOK{Gropp1994a, author = "William D.~Gropp and Ewing Lusk and Anthony Skjellum", editor = "", year = 1994, title = "Using MPI -- Portable Parallel Programming with the Message Passing Interface", booktitle = "", series = "", number = "", note = "", publisher = "MIT Press", address = "Cambridge", key = "Gropp1994a", abstract = "", comment = "", keywords = "", referred = "[Lee2001a].", isbn = "" } @ARTICLE{Gropp1996a, author = "William D.~Gropp and Ewing Lusk and Nathan Doss and Anthony Skjellum", month = "", year = 1996, title = "A High-Performance Portable Implementation of the {MPI} Message Passing Interface Standard", journal = "Parallel Computing", volume = 22, number = "", pages = "789--828", note = "", key = "Gropp1996a", abstract = "", comment = "", keywords = "", referred = "[Carle2001a]." } @BOOK{Gropp1998b, author = "William D.~Gropp and Steven Huss-Lederman and Andrew Lumsdaine and Ewing Lusk and Bill Nitzberg and William Saphir and Marc Snir", editor = "", year = 1998, title = "MPI: The Complete Reference, Volume 2, The {MPI-2} Extensions", series = "", number = "", note = "", publisher = "MIT Press", address = "", key = "Gropp1998b", abstract = "", comment = "", keywords = "", referred = "[Carle2001a].", isbn = 0262571234 } @INPROCEEDINGS{Gropp2000a, author = "William D. Gropp and Dinesh K. Kaushik and David E. Keyes and Barry F. Smith", editor = "", year = 2000, title = "Performance Modeling and Tuning of an Unstructured Mesh {CFD} Application", booktitle = "Proceedings of SC2000", series = "", number = "", pages = "", note = "", publisher = "IEEE Computer Society", address = "", key = "Gropp2000a", abstract = "", comment = "", keywords = "", referred = "[Keyes2001a]." } @ARTICLE{Gropp2000b, author = "William D.~Gropp and David E.~Keyes and Lois C. McInnes and M.~D.~Tidriri", year = 2000, title = "Globalized {N}ewton-{K}rylov-{S}chwarz Algorithms and Software for Parallel Implicit {CFD}", journal = "Int. J. High Performance Computing Applications", volume = 14, pages = "102--136", key = "Gropp2000b", type = "", abstract = "", comment = "", keywords = "", referred = "[Abate2001a]." } @INCOLLECTION{Guckenheimer1996a, author = "John Guckenheimer", editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank", year = 1996, title = "Bifurcations, Automatic Differentiation and Computer Generated Proofs", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "229--237", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Guckenheimer1996a", crossref = "Berz1996c", abstract = "Dynamical systems theory relies upon coordinate transformations to study qualitative properties of vector fields. These coordinate transformations depend upon derivatives of the vector fields as well as the values of the vector fields. Thus, automatic differentiation provides an attractive technology for studying dynamical systems. This paper describes one novel area in which this appears to be the case: computer validation of the phase portraits for families of planar vector fields. Hilbert's sixteenth problem is used to motivate interest in these results. The discussion is informal and new results are only sketched since the new algorithms for verifying properties of bifurcations have not been implemented and tested on examples.", comment = "", keywords = "Dynamical systems, bifurcation, computer validation, phase portraits, Hilbert's sixteenth problem.", referred = "" } @ARTICLE{Guillaume1994a, author = "Philippe Guillaume and Mohamed Masmoudi", month = "", year = 1994, title = "Computation of Higher Order Derivatives in Optimal Shape Design", journal = "Numerische Mathematik", volume = 67, number = "", pages = "231--250", note = "", key = "Guillaume1994a", abstract = "", comment = "", keywords = "", referred = "[Beley2001a], [Evtushenko2001a]." } @INCOLLECTION{Haase2001a, author = "Gundolf Haase and Ulrich Langer and Ewald Lindner and Wolfram M{\"u}hlhuber", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Optimal Sizing of Industrial Structural Mechanics Problems Using AD", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 21, pages = "181--188", note = "", publisher = "Springer", address = "New York", key = "Haase2001a", crossref = "Corliss2001b", abstract = "We consider minimizing the mass of the frame of an injection moulding machine as an example of optimal sizing. The deformation of the frame is described by a generalized plane stress state with an elasticity modulus scaled by the thickness. The resulting constrained nonlinear optimization problem is solved by sequential quadratic programming (SQP), which requires gradients of the objective and the constraints with respect to the design parameters. As long as the number of design parameters is small, finite differences may be used. For several hundreds of varying thickness parameters, we use the reverse mode of automatic differentiation (AD). AD works fine but requires huge memory and disk capabilities and limits the use of iterative solvers for the governing state equations. Therefore, we combine AD with the adjoint method to get a fast and flexible hybrid gradient evaluation procedure. Numerical results show the potential of this approach and imply that this method can also be used for finding an initial guess for a shape optimization.", comment = "", keywords = "", referred = "[Klein2001a].", isbn = "" } @BOOK{Haftka1992a, author = "Raphael T. Haftka and Zafer G{\"u}rdal", editor = "", year = 1992, title = "Elements of Structural Optimization", series = "", number = "", note = "", publisher = "Kluwer Academic Publishers", address = "Dordrecht", key = "Haftka1992a", abstract = "", comment = "", keywords = "", referred = "[Dignath2001a].", isbn = "" } @INCOLLECTION{Hague2001a, author = "Steve Hague and Uwe Naumann", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Present and Future Scientific Computation Environments", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 5, pages = "59--66", note = "", publisher = "Springer", address = "New York", key = "Hague2001a", crossref = "Corliss2001b", abstract = "Problem Solving Environments and Environments for Scientific Computing play an increasingly important role in the modelling, simulation, and optimization of real-world applications. This paper will discuss some of the experiences made through the involvement of NAG Ltd. in several European projects aiming towards the development of such tools. It will also note some of the encouraging developments, particularly in the area of interface standards that might make PSE construction a more effective and realistic prospect in the future.", comment = "", keywords = "", referred = "", isbn = "" } @TECHREPORT{Hall1984a, author = "Michael G. Hall", month = "December", year = 1984, title = "Cell-Vertex Multigrid Solution of the {E}uler Equations for Transonic Flow Past Aerofoils", number = 84116, note = "", address = "", institution = "Royal Aircraft Establishment", key = "Hall1984a", type = "{T}echnical {R}eport", abstract = "", comment = "", keywords = "", referred = "[Forth2001a]." } @ARTICLE{Hamilton1986a, author = "D. C. Hamilton", month = "", year = 1986, title = "Confidence Regions for Parameter Subsets in Nonlinear Regression", journal = "Biometrika", volume = 73, number = "", pages = "57--64", note = "", key = "Hamilton1986a", abstract = "", comment = "", keywords = "", referred = "[Huiskes2001a]." } @BOOK{Hansen1986a, author = "Jean-Pierre Hansen", editor = "", year = 1986, title = "Theory of Simple Liquids", series = "", number = "", note = "", publisher = "Academic Press", address = "", key = "Hansen1986a", abstract = "", comment = "", keywords = "", referred = "[Charpentier2001a].", isbn = "" } @BOOK{Hansen1992a, author = "Elden R. Hansen", year = 1992, title = "Global Optimization Using Interval Analysis", series = "", number = "", publisher = "Marcel Dekker", address = "New York", key = "Hansen1992a", abstract = "", comment = "", keywords = "", referred = "[Jerrell1996a], [Kearfott2001a], [Rall1996a].", isbn = 0824786963 } @INCOLLECTION{Hascoet2001a, author = "Laurent Hasco{\"e}t and Stefka Fidanova and Christophe Held", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Adjoining Independent Computations", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 35, pages = "299--304", note = "", publisher = "Springer", address = "New York", key = "Hascoet2001a", crossref = "Corliss2001b", abstract = "The {\em reverse} or {\em adjoint} mode of automatic differentiation is a software engineering technique that permits efficient computation of gradients. However, this technique requires a lot of temporary memory. In this paper, we present a refinement that reduces memory consumption in the case of parallel loops, and we give a proof of its correctness based on properties of the {\em data-dependence graph} of adjoint programs and parallel loops. This technique is particularly suitable for assembly loops that dominate in mesh-based computations. Application is done on the kernel of a realistic Navier-Stokes solver.", comment = "", keywords = "", referred = "[Mancini2001a], [Souli\'e2001a].", isbn = "" } @TECHREPORT{Hascoet2001b, author = "Laurent Hasco{\"e}t", year = 2001, title = "The Data-Dependence Graph of Adjoint Programs", number = 4167, note = "See \url{www.inria.fr/rrrt/rr-4167.html}.", address = "Sophia-Antipolis, France", institution = "INRIA", key = "Hascoet2001b", type = "Research Report", referred = "[Hascoet20012001a]." } @BOOK{Haslinger1988a, author = "Jaroslav Haslinger and Pekka Neittaanm{\"a}ki", editor = "", year = 1988, title = "Finite Element Approximation for Optimal Shape Design: {T}heory and Applications", series = "", number = "", note = "", publisher = "John Wiley \& Sons Ltd.", address = "Chichester", key = "Haslinger1988a", abstract = "", comment = "", keywords = "", referred = "[Haase2001a].", isbn = "" } @INCOLLECTION{Hassold1996a, author = "Eric Hassold and Andr{\'e} Galligo", editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank", year = 1996, title = "Automatic Differentiation Applied to Nonsmooth Convex Optimization", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "287--297", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Hassold1996a", crossref = "Berz1996c", abstract = "In several applications, one is led to minimize a nonlinear function $f$ that is differentiable or at least admits gradients almost everywhere. In this paper, we outline optimization algorithms that rely on explicit computations of gradients or limits of gradients, using specific automatic differentiation techniques. We consider functions represented by Fortran programs. We suppose that singularities are consequences either of ``branching'' operations (absolute value, max, conditional structures with simple tests) or of classical elementary functions (square root when computing an Euclidean norm), which generate kinks where $f$ admits a directional derivative in any direction. We present algorithms and implementations on top of the automatic differentiation system Odyss\'ee to compute directional derivatives and limits of gradients that allow descriptions of normal cones. Together with the input Fortran code, this is used by our optimization library Odymin to minimize $f$. Finally, we discuss the capability, efficiency, and extensibility of our approach. We compare the number of calls required by different strategies for a classical exampl", comment = "", keywords = "Optimization, nonsmooth optimization, directional Taylor expansion, convex optimization, bundle methods, Odyss\'ee.", referred = "[Berz2001a], [Dignath2001a]." } @ARTICLE{Hendrikx1996a, author = "J.~P.~M.~Hendrikx and T.~J.~J.~Meijlink and R.~F.~C.~Kriens", month = "", year = 1996, title = "Application of Optimal Control Theory to Inverse Simulation of Car Handling", journal = "Vehicle System Dynamics", volume = 26, number = 6, pages = "449--462", note = "", key = "Hendrikx1996a", abstract = "", comment = "", keywords = "", referred = "[Casanova2001a]." } @ARTICLE{Hibler1980a, author = "W.~D.~{Hibler, III}", month = "", year = 1980, title = "Modeling a Variable Thickness Sea-Ice Cover", journal = "Mon.~Wea.~Rev.", volume = 108, number = "", pages = "1943--1973", note = "", key = "Hibler1980a", abstract = "", comment = "", keywords = "", referred = "" } @TECHREPORT{Hillstrom1985a, author = "Kenneth E. Hillstrom", year = 1985, title = "Users Guide for {JAKEF}", number = "ANL/MCS--TM--16", address = "Argonne, Ill.", institution = "Mathematics and Computer Science Division, Argonne National Laboratory", key = "Hillstrom1985a", type = "Technical Memorandum", abstract = "", comment = "", keywords = "", referred = "[Corliss1991a]; [Garcia1991a]; [Goldman91a]; [Irim1991a]; [Juedes1991a]; [Kubota1991a]; [Souli\'e1991a], [Tijskens2001a]." } @TECHREPORT{Hindmarsh1999a, author = "Alan C.~Hindmarsh and Allan G.~Taylor", month = "", year = 1999, title = "User Documentation for {IDA}, a Differential-Algebraic Equation Solver for Sequential and Parallel Computers", number = "UCRL-MA-136910", note = "", address = "", institution = "Lawrence Livermore National Laboratory", key = "Hindmarsh1999a", type = "", abstract = "", comment = "", keywords = "", referred = "[Lee2001a]." } @BOOK{Hochbaum1997a, author = "", editor = "Dorit S.~Hochbaum", year = 1997, title = "Approximation Algorithms for {NP}-Hard Problems", series = "", number = "", note = "", publisher = "PWS Publishing Company", address = "20 Park Plaza, Boston", key = "Hochbaum1997a", abstract = "", comment = "", keywords = "", referred = "[Griewank2001a].", isbn = "" } @ARTICLE{Hoefkens2000a, author = "Jens Hoefkens and Martin Berz", editor = "", year = "to appear, 2001", title = "Verification of Invertibility and Charting of Constraint Manifolds in {DAE}s", booktitle = "Proceedings, Sixth International Conference on Applications of Computer Algebra", series = "", journal = "Reliable Computing", number = "", pages = "", note = "Special issue: Proceedings of the Sixth International Conference on Applications of Computer Algebra.", publisher = "", address = "", key = "Hoefkens2000a", abstract = "", comment = "", keywords = "", referred = "[Hoefkens2001a]." } @INCOLLECTION{Hoefkens2001a, author = "Jens Hoefkens and Martin Berz and Kyoko Makino", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Efficient High-Order Methods for {ODE}s and {DAE}s", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 41, pages = "343--348", note = "", publisher = "Springer", address = "New York", key = "Hoefkens2001a", crossref = "Corliss2001b", abstract = "We present methods for the high-order differentiation through ordinary differential equations (ODEs), and more importantly, differential algebraic equations (DAEs). First, methods are developed that assert that the requested derivatives are really those of the solution of the ODE, and not those of the algorithm used to solve the ODE. Next, high-order solvers for DAEs are developed that in a fully automatic way turn an $n$-th order solution step of the DAEs into a corresponding step for an ODE initial value problem. In particular, this requires the automatic high-order solution of implicit relations, which is achieved using an iterative algorithm that converges to the exact result in at most $n+1$ steps. We give examples of the performance of the method.", comment = "", keywords = "", referred = "", isbn = "" } @ARTICLE{Holland1993a, author = "D.~M.~Holland and L.~A.~Mysak and D.~K.~Manak", month = "", year = 1993, title = "Sensitivity Study of a Dynamic-Thermodynamic Sea-Ice Model", journal = "J.~Geophys.~Res.", volume = 98, number = "", pages = "2561--2586", note = "", key = "Holland1993a", abstract = "", comment = "", keywords = "", referred = "[Kim2001a]." } @BOOK{Horowitz1978a, author = "E. Horowitz and P. Sahni", editor = "", year = 1978, title = "Fundamentals of Computer Algorithms", series = "", number = "", note = "", publisher = "Computer Science Press", address = "", key = "Horowitz1978a", abstract = "", comment = "", keywords = "", referred = "[Naumann2001a].", isbn = "" } @TECHREPORT{Horwedel1988a, author = "Jim E. Horwedel and Brian A. Worley and E. M. Oblow and F. G. Pin", year = 1988, title = "{GRESS} version 1.0 Users Manual", number = "ORNL/TM 10835", address = "Oak Ridge, Tenn.", institution = "Martin Marietta Energy Systems, Inc., Oak Ridge National Laboratory", key = "Horwedel1988a", type = "Technical Memorandum", abstract = "", comment = "", keywords = "", referred = "[Goldman1991a]; [Horwedel1991a]; [Irim1991a]; [Juedes1991a]; [Souli\'e1991a], [Tijskens2001a]." } @INCOLLECTION{Horwedel1991a, author = "Jim E.~Horwedel", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "{GRESS}: {A} Preprocessor for Sensitivity Studies on {F}ortran Programs", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "243--250", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Horwedel1991a", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "[Shirieav1996a].", isbn = "0--89871--284--X" } @ARTICLE{Hossain1998a, author = "A.K.M.~Shahadat Hossain and Trond Steihaug", month = "", year = 1998, title = "Computing a Sparse {J}acobian Matrix by Rows and Columns", journal = "Optimization Methods and Software", volume = 10, number = "", pages = "33--48", note = "", key = "Hossain1998a", abstract = "", comment = "", keywords = "", referred = "[Griewank2001a]." } @PHDTHESIS{Hossain1998b, author = "A.K.M.~Shahadat Hossain", month = "", year = 1998, title = "On the {C}omputation of {S}parse {J}acobian {M}atrices and {N}ewton {S}teps", note = "Technical Report 146.", address = "", school = "Department of Informatics, University of Bergen", key = "Hossain1998b", abstract = "", comment = "", keywords = "", referred = "[Hossain2001a]." } @INCOLLECTION{Hossain2001a, author = "Shahadat Hossain and Trond Steihaug", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Reducing the Number of {AD} Passes for Computing a Sparse {J}acobian Matrix", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 31, pages = "263--270", note = "", publisher = "Springer", address = "New York", key = "Hossain2001a", crossref = "Corliss2001b", abstract = "A reduction in the computational work is possible if we do not require that the nonzeros of a Jacobian matrix be determined directly. If a column or row partition is available, the proposed substitution technique can be used to reduce the number of groups in the partition further. In this chapter, we present a substitution method to determine the structure of sparse Jacobian matrices efficiently using forward, reverse, or a combination of forward and reverse modes of AD. Specifically, if it is true that the difference between the maximum number of nonzeros in a column or row and the number of groups in the corresponding partition is large, then the proposed method can save many AD passes. This assertion is supported by numerical examples.", comment = "", keywords = "", referred = "[Klein2001a].", isbn = "" } @TECHREPORT{Hovland1997a, author = "Paul D.~Hovland and Michael T.~Heath", month = "", year = 1997, title = "Adaptive {SOR}: A Case Study in Automatic Differentiation of Algorithm Parameters", number = "ANL/MCS-P673-0797", note = "", address = "", institution = "Mathematics and Computer Science Division, Argonne National Laboratory", key = "Hovland1997a", type = "", abstract = "", comment = "", keywords = "", referred = "[Kim2001a]." } @PHDTHESIS{Hovland1997b, author = "Paul D.~Hovland", month = "May", year = 1997, title = "Automatic Differentiation of Parallel Programs", note = "", address = "Urbana, Ill.", school = "University of Illinois at Urbana-Champaign", key = "Hovland1997b", abstract = "", comment = "", keywords = "", referred = "[Abate2001a], [Lee2001a], [Mancini2001a]." } @TECHREPORT{Hovland1997c, author = "Paul D. Hovland and Bijan Mohammadi and Christian H. Bischof", month = "", year = 1997, title = "Automatic Differentiation of {N}avier-{S}tokes Computations", number = "MCS-P687-0997", note = "", address = "", institution = "Argonne National Laboratory", key = "Hovland1997c", type = "", abstract = "", comment = "", keywords = "", referred = "[Hascoet2001a]." } @INPROCEEDINGS{Hovland1998a, author = "Paul D.~Hovland and Christian H.~Bischof", editor = "", year = 1998, title = "Automatic Differentiation of Message-Passing Parallel Programs", booktitle = "Proceedings of the First Merged International Parallel Processing Symposium and Symposium on Parallel and Distributed Processing", series = "", number = "", pages = "98--104", note = "", publisher = "IEEE Computer Society Press", address = "Los Alamitos, CA", key = "Hovland1998a", abstract = "", comment = "", keywords = "", referred = "[Abate2001a], [Lee2001a]." } @INPROCEEDINGS{Hovland1998b, author = "Paul D.~Hovland and Boyana Norris and Lucas Roh and Barry F.~Smith", editor = "", year = 1999, title = "Developing a Derivative-Enhanced Object-Oriented Toolkit for Scientific Computations", booktitle = "Proceedings of the SIAM Workshop on Object Oriented Methods for Inter-operable Scientific and Engineering Computing", series = "", number = "", pages = "129--137", note = "", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Hovland1998b", abstract = "", comment = "", keywords = "", referred = "[Abate2001a], [Lee2001a]." } @TECHREPORT{Hovland2000b, author = "Paul D.~Hovland and Lois C. McInnes", month = "", year = 2000, title = "Parallel Simulation of Compressible Flow Using Automatic Differentiation and {PETSc}", number = "ANL/MCS-P796-0200", note = "To appear in a special issue of {\sl Parallel Computing\/} on ``Parallel Computing in Aerospace''", address = "", institution = "Mathematics and Computer Science Division, Argonne National Laboratory", key = "Hovland2000b", type = "", abstract = "", comment = "", keywords = "", referred = "[Abate2001a]." } @INCOLLECTION{Huiskes1998a, author = "Mark J. Huiskes", editor = "F. {Funk et al.}", year = 1998, title = "Virtual Population Analysis with the Adjoint Method", booktitle = "Fishery Stock Assessment Models", series = "", number = "", pages = "639--658", note = "", publisher = "Alaska Sea Grant College Program Report No. AK-SG-98-01", address = "University of Alaska, Fairbanks", key = "Huiskes1998a", abstract = "", comment = "", keywords = "", referred = "[Huiskes2001a]." } @INCOLLECTION{Huiskes2001a, author = "Mark J. Huiskes", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Automatic Differentiation for Modern Nonlinear Regression", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 8, pages = "83--90", note = "", publisher = "Springer", address = "New York", key = "Huiskes2001a", crossref = "Corliss2001b", abstract = "For modern nonlinear regression routines, the efficient computation of first and higher order derivatives is highly important. Automatic differentiation constitutes an opportunity to achieve both higher run-time efficiency and an increased feasibility of higher-order uncertainty analysis of complex models. In this article we present an overview of the derivative requirements of nonlinear regression routines. We further describe our experience in developing a C++ library for model analysis that uses the ADOL-C package for automatic differentiation. We show how the model analysis library, named MAP, has benefited from using automatic differentiation. Also a number of experiments are presented to show how more flexible and efficient execution trace management could further enhance the ease-of-use of ADOL-C.", comment = "", keywords = "", referred = "[Klein2001a].", isbn = "" } @ARTICLE{Huiskes2001b, author = "Mark J. Huiskes", month = "", year = 2001, title = "Evaluation of Parametric and Structural Uncertainty in Stock Assessment Models with an Application to {N}orth {S}ea Herring", journal = "Canadian Journal of Fisheries and Aquatic Sciences", volume = "", number = "", pages = "", note = "Submitted.", key = "Huiskes2001b", abstract = "", comment = "", keywords = "", referred = "[Huiskes2001a]." } @ARTICLE{Hunke1997a, author = "E.~C.~Hunke and J.~K.~Dukowicz", month = "", year = 1997, title = "An Elastic-Viscous-Plastic Model for Sea-Ice Dynamics", journal = "J.~Phys.~Oceanog.", volume = 27, number = "", pages = "1849--1867", note = "", key = "Hunke1997a", abstract = "", comment = "", keywords = "", referred = "[Kim2001a]." } @INCOLLECTION{Hutschenreiter1996a, author = "Ulf Hutschenreiter", editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank", year = 1996, title = "A New Method for Bevel Gear Tooth Flank Computation", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "329--341", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Hutschenreiter1996a", crossref = "Berz1996c", abstract = "The use of automatic differentiation for an exact computation of geometric properties of bevel gear tooth flanks is discussed. Known models of the kinematics of the machine tools generating bevel gear tooth flanks have been improved. Using that result, we compute curvature properties of the generated envelope surfaces directly. From an analytical point of view, the envelope condition used in differential geometry can be interpreted as a singularity of a vector function in 3-space. By an analytical characterization of this singularity we obtain a two-dimensional parameterization of the generated flank for any machine parameter set. The necessary partial derivatives of the vector function are computed with the help of automatic differentiation. For the first time it is possible to compute the curvature properties and the resulting undercut geometry between tooth and fillet surface of the tooth flanks of any spiral bevel or hypoid gear without any approximation.", comment = "", keywords = "Spiral bevel gears, hypoid gears, tooth flank computation, undercutting, edge of regression, envelope condition, derivative tensors, higher order differentiation, cusp singularities.", referred = "" } @BOOK{IEEE1985a, author = "{IEEE}", editor = "", year = 1985, title = "{IEEE} Standard for Binary Floating-Point Arithmetic, {ANSI/IEEE} Standard 754-1985", series = "", number = "", note = "Reprinted in SIGPLAN Notices, 22(2):9--25, 1987", publisher = "Institute of Electrical and Electronics Engineers", address = "New York", key = "IEEE1985a", abstract = "", comment = "", keywords = "", referred = "[Braconnier2001a].", isbn = "" } @TECHREPORT{Iri1987a, author = "Masao Iri and Koichi Kubota", year = 1987, title = "Methods of Fast Automatic Differentiation and Applications", number = "RMI 87 -- 02", address = "", institution = "Department of Mathematical Engineering and Information Physics, Faculty of Engineering, University of Tokyo", key = "Iri1987a", type = "Research Memorandum", abstract = "", comment = "", keywords = "", referred = "[Evtushenko1991a], [Fischer1991b], [Goldman1991a], [Irim1991a], [Kubota1991a], [Kubota1996a], [Juedes1991a], [Tijskens2001a]." } @INCOLLECTION{Iri1991a, author = "Masao Iri", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "History of Automatic Differentiation and Rounding Estimation", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "1--16", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Iri1991a", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "[Bischof1996b], [Braconnier2001a], [Chavent1996a], [Feehery1996a], [Klein2001a], [Rall1996a].", isbn = "0--89871--284--X" } @BOOK{Isidori1995a, author = "Alberto Isidori", editor = "", year = 1995, title = "Nonlinear Control Systems: An Introduction", edition = "third", series = "", number = "", note = "", publisher = "Springer-Verlag", address = "Berlin", key = "Isidori1995a", abstract = "", comment = "", keywords = "", referred = "[Dignath2001a], [R{\"o}benack2001a].", isbn = "" } @ARTICLE{Iwasaki1974a, author = "Machio Iwasaki", month = "", year = 1974, title = "Second-Order Perturbation Treatment of the General Spin {H}amiltonian in an Arbitrary Coordinate System", journal = "Journal of Magnetic Resonance", volume = 16, number = "", pages = "417--423", note = "", key = "Iwasaki1974a", abstract = "", comment = "", keywords = "", referred = "[Souli\'e2001a]." } @PHDTHESIS{Jacob1997a, author = "R.~Jacob", month = "", year = 1997, title = "Low Frequency Variability of the Atmosphere-Ocean System", note = "", address = "Madison", school = "Univ. of Wisconsin", key = "Jacob1997a", abstract = "", comment = "", keywords = "", referred = "[Kim2001a]." } @BOOK{Jacobson1970a, author = "D. H. Jacobson and D. Q. Mayne", editor = "", year = 1970, title = "Differential Dynamic Programming", booktitle = "", series = "", number = "", note = "", publisher = "American Elsevier", address = "New York", key = "Jacobson1970a", abstract = "", comment = "", keywords = "", referred = "[Christianson2001a].", isbn = "" } @INPROCEEDINGS{Jameson1999a, author = "Antony Jameson and John Vassberg", editor = "", year = 1999, title = "Studies of Alternate Numerical Optimization Methods Applied to the Brachistochrone Problem", booktitle = "OptiCON '99 Conference", series = "", number = "", pages = "", note = "", publisher = "", address = "", key = "Jameson1999a", abstract = "", comment = "", keywords = "", referred = "[Giles2001a]." } @INCOLLECTION{Jerrell1996a, author = "Max E.~Jerrell", editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank", year = 1996, title = "Automatic Differentiation and Interval Arithmetic for Estimation of Econometric Functions", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "265--272", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Jerrell1996a", crossref = "Berz1996c", abstract = "Relatively simple economic models often lead to complex estimation problems. Even when the model itself is linear, the estimation problem can be nonlinear, with an unknown number of stationary points. Disequilibrium models have proved to be particularly difficult to estimate. Newer global optimization techniques, such as simulated annealing and genetic algorithms, have not been particularly successful in solving such models. More traditional methods can fail completely unless good starting points are used. The gradient vectors and Hessian matrices of nonlinear econometric functions tend to be complex and lead to well known user and computational approximation errors. Automatic differentiation can eliminate user error. Combined with interval arithmetic, it offers a particularly useful method of global optimization.", comment = "", keywords = "interval computations, global optimization, econometrics, disequilibrium models", referred = "" } @ARTICLE{Jessani1998a, author = "R. Jessani and M. Putrino", month = "", year = 1998, title = "Comparison of Single- and Dual-Pass Multiply-Add Fused Floating-Point Units", journal = "IEEE Trans. on Computers", volume = 47, number = 9, pages = "", key = "Jessani1998a", abstract = "", comment = "", keywords = "", referred = "[Naumann2001a]." } @BOOK{Jiang1998a, author = "Bo-Nan Jiang", editor = "", year = 1998, title = "The Least-Squares Finite Element Method, Theory and Applications in Computational Fluid Dynamics and Electromagnetics", series = "Scientific Computation", number = "", note = "", publisher = "Springer", address = "", key = "Jiang1998a", abstract = "", comment = "", keywords = "", referred = "[Tijskens2001a].", isbn = 3540639349 } @INPROCEEDINGS{Jouhanique1995a, author = "T.~Jouhanique and Paul Rascle", editor = "R.~C.~Block and F.~Feiner", year = 1995, title = "A Fifth Equation to Model the Relative Velocity in the {3--D} Thermal-Hydraulic Code {THYC}.", booktitle = "Proceedings of the Sixth Nuclear Reactor Thermal-Hydraulic (NURETH) Congress", series = "", number = "", pages = "", note = "", publisher = "American Nuclear Society, Nuclear Regulatory Commission Publication.", address = "", key = "Jouhanique1995a", abstract = "", comment = "", keywords = "", referred = "[Faure2001a]." } @MISC{JPL2000a, author = "{Jet Propulsion Laboratory}", month = "", year = "", title = "{JPL} {S}olar {S}ystem {D}ynamics", note = "See \url{ssd.jpl.nasa.gov}", howpublished = "", key = "JPL2000a", abstract = "", comment = "", keywords = "", referred = "[Makino2001a]." } @INCOLLECTION{Juedes1991a, author = "David W.~Juedes", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "A Taxonomy of Automatic Differentiation Tools", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "315--329", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Juedes1991a", crossref = "Griewank1991e", abstract = "", comment = "Also appeared as Preprint MCS--P265--0991, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill., September 1991.", keywords = "", referred = "[Goldman1996a], [Rall1996a].", isbn = "0--89871--284--X" } @INCOLLECTION{Juedes1996a, author = "David W.~Juedes and Karthik Balakrishnan", editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank", year = 1996, title = "Generalized Neural Networks, Computational Differentiation, and Evolution", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "273--285", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Juedes1996a", crossref = "Berz1996c", abstract = "Backpropagation is a powerful and widely used procedure for training multilayer, feedforward artificial neural networks. The procedure can be seen as a special case of the reverse mode of computational differentiation. This connection between backpropagation and computational differentiation leads us to envision a scenario wherein neural networks can be trained by using gradient descent methods and computational differentiation tools like ADOL--C. The primary advantage offered by such an approach is the possibility of training networks consisting of heterogeneous functional units---a notion we refer to as {\em generalized neural networks.} This approach, in conjunction with {\em evolutionary algorithms,} can be used to produce near-optimal designs. This paper presents this approach in more detail and demonstrates its usefulness through simulation results.", comment = "", keywords = "Neural networks, genetic algorithms, evolution, ADOL--C.", referred = "" } @INCOLLECTION{Kalman1991a, author = "Dan Kalman and Robert Lindell", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "Automatic Differentiation in Astrodynamical Modeling", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "228--243", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Kalman1991a", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "", isbn = "0--89871--284--X" } @INCOLLECTION{Kearfott1996a, author = "R.~Baker Kearfott", editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank", year = 1996, title = "Automatic Differentiation of Conditional Branches in an Operator Overloading Context", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "75--81", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Kearfott1996a", crossref = "Berz1996c", abstract = "In the past, it has been problematical to include {\tt IF-THEN-ELSE} branches in automatic differentiation processes driven by operator overloading and code list generation, when the branch condition contains variables. However, this problem can be circumvented with a special ``branch function'' $\chi$. Definition of this function, formulas for its use, and implications of its use will be discussed. A second issue is: what can be done when derivatives are discontinuous? In fact, simple and meaningful Newton iterations can be set up when even the function itself is discontinuous. Simplified figures and examples are given, as well as references to in-depth explanations. An example of the convergence behavior is given with an interval Newton method to find critical points for the problem ``$\min |x|$.''", comment = "", keywords = "Conditional branches, operator overloading, branch function, discontinuous derivatives.", referred = "[Berz2001a], [Dignath2001a]." } @BOOK{Kearfott1996b, author = "R.~Baker Kearfott", year = 1996, title = "Rigorous Global Search: Continuous Problems", series = "", number = "", publisher = "Kluwer Academic Publishers", address = "Dordrecht, Netherlands", key = "Kearfott1996b", abstract = "", comment = "", keywords = "", referred = "[Jerrell1996a], [Kearfott1996a].", isbn = "0--7923--4238--0" } @ARTICLE{Kearfott1997a, author = "R. Baker Kearfott", month = "", year = 1997, title = "Empirical Evaluation of Innovations in Interval Branch and Bound Algorithms for Nonlinear Algebraic Systems", journal = "SIAM J. Sci. Comput.", volume = 18, number = 2, pages = "574--594", note = "", key = "Kearfott1997a", abstract = "", comment = "", keywords = "", referred = "[Kearfott2001a]." } @ARTICLE{Kearfott2000a, author = "R. Baker Kearfott", year = 2000, title = "On Stopping Criteria in Verified Nonlinear Systems or Optimization Algorithms", journal = "ACM Trans. Math. Software", volume = 26, number = 3, pages = "373--389", note = "", key = "Kearfott2000a", abstract = "", comment = "", keywords = "", referred = "[Kearfott2001a]." } @INCOLLECTION{Kearfott2001a, author = "R.~Baker Kearfott and Alvard Arazyan", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Taylor Series Models in Deterministic Global Optimization", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 44, pages = "365--372", note = "", publisher = "Springer", address = "New York", key = "Kearfott2001a", crossref = "Corliss2001b", abstract = "Deterministic global optimization requires a global search with rejection of subregions. To reject a subregion, bounds on the range of the constraints and objective function can be used. Although often effective, simple interval arithmetic sometimes gives impractically large bounds on the ranges. However, Taylor models as developed by Berz et al. may be effective in this context. Efficient incorporation of such models in a general global optimization package is a significant project. Here, we use the system COSY Infinity by Berz et al. to study the bounds on the range of various order Taylor models for certain difficult test problems we have previously encountered. Based on that, we conclude that Taylor models may be useful for some, but not all, problems in verified global optimization. Forthcoming improvements in the COSY Infinity interface will help us reach stronger conclusions.", comment = "", keywords = "", referred = "[Makino2001a].", isbn = "" } @ARTICLE{Kelley1998a, author = "C. T. Kelley and David E. Keyes", month = "", year = 1998, title = "Convergence Analysis of Pseudo-Transient Continuation", journal = "SIAM J. Numer. Anal.", volume = 35, number = "", pages = "508--523", note = "", key = "Kelley1998a", abstract = "", comment = "", keywords = "", referred = "[Keyes2001a]." } @ARTICLE{Keyes1987a, author = "David E. Keyes and William D. Gropp", month = "", year = 1987, title = "A Comparison of Domain Decomposition Techniques for Elliptic Partial Differential Equations and their Parallel Implementation", journal = "SIAM J. Sci. Stat. Comput.", volume = 8, number = 2, pages = "s166--s202", note = "", key = "Keyes1987a", abstract = "", comment = "", keywords = "", referred = "[Keyes2001a]." } @INCOLLECTION{Keyes2001a, author = "David E.~Keyes and Paul D.~Hovland and Lois C. McInnes and Widodo Samyono", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Using Automatic Differentiation for Second-order Matrix-free Methods in {PDE}-Constrained Optimization", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 3, pages = "35--50", note = "", publisher = "Springer", address = "New York", key = "Keyes2001a", crossref = "Corliss2001b", abstract = "Classical methods of constrained optimization are often based on the assumptions that projection onto the constraint manifold is routine, but accessing second-derivative information is not. Both assumptions need revision for the application of optimization to systems constrained by partial differential equations, in the contemporary limit of millions of state variables and in the parallel setting. Large-scale PDE solvers are complex pieces of software that exploit detailed knowledge of architecture and application and cannot easily be modified to fit the interface requirements of a blackbox optimizer. Furthermore, in view of the expense of PDE analyses, optimization methods not using second derivatives may require too many iterations to be practical. For general problems, automatic differentiation is likely to be the most convenient means of exploiting second derivatives. We delineate a role for automatic differentiation in matrix-free optimization formulations involving Newton's method, in which little more storage is required than that for the analysis code alone.", comment = "", keywords = "", referred = "[Mor\'e2001a].", isbn = "" } @INCOLLECTION{Kim2001a, author = "Jong G.~Kim and Paul D.~Hovland", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Sensitivity Analysis and Parameter Tuning of a Sea-Ice Model", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 9, pages = "91--98", note = "", publisher = "Springer", address = "New York", key = "Kim2001a", crossref = "Corliss2001b", abstract = "The values of many of the parameters in climate models are often not known with any great precision. We describe the use of automatic differentiation to examine the sensitivity of an uncoupled dynamic-thermodynamic sea-ice model to various parameters. We also illustrate the effectiveness of using these sensitivity derivatives with an optimization algorithm to tune the parameters to maximize the agreement between simulated results and observational data.", comment = "", keywords = "", referred = "[Haase2001a], [Klein2001a].", isbn = "" } @BOOK{Kirk1970a, author = "D.~E.~Kirk", editor = "", year = 1970, title = "Optimal Control Theory: An Introduction", series = "", number = "", note = "", publisher = "Prentice Hall", address = "Englewood Cliffs, New Jersey", key = "Kirk1970a", abstract = "", comment = "", keywords = "", referred = "[Casanova2001a].", isbn = "" } @ARTICLE{Klein1995a, author = "Wolfram Klein", month = "", year = 1995, title = "Report on Symbolic Manipulators for Automatic Code Generation. {EG} Project {Jessi AC} 12: {A}nalog Expert Design System", journal = "Milestone Report", volume = "", number = "", pages = "", key = "Klein1995a", abstract = "", comment = "", keywords = "", referred = "[Klein1996a], [Klein2001a]." } @INCOLLECTION{Klein1996a, author = "Wolfram Klein", editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank", year = 1996, title = "Comparisons of Automatic Differentiation Tools in Circuit Simulation", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "297--307", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Klein1996a", crossref = "Berz1996c", abstract = "Simulation models for semiconductor elements like MOS transistors are of great interest in the field of circuit simulation (MOS : metal oxide semiconductor). Because of the nonlinearity of the terminal current and charge functions with respect to the input voltages, the derivatives of these transistor functions are needed In this paper, we compare different automatic differentiation (AD) tools in a concrete application of large transistor models. First, results using the method of differentiation `by hand` are shown. Then, results are presented for the application of the AD tools ADIFOR, Odyss{\'e}e, and the Fortran 90 extension ADOL--F to MOS transistor simulation models. On a higher level of modeling (i.e., on the functional description itself), an operator-based system SYPERB using the programming language PASCAL-XSC is proposed. This tool enables not only reading, creating, and evaluation of the mathematical formulas, but also differentiation using different kinds of arithmetics as well as the forward or the reverse mode of automatic differentiation.", comment = "", keywords = "Circuit simulation, transistor models, ADIFOR, Odyss{\'e}e, ADOL--F, SYPERB.", referred = "[Klein2001a]." } @INPROCEEDINGS{Klein1996b, author = "Wolfram Klein", editor = "", year = 1996, title = "Symbolic Modeling in Circuit Simulation", booktitle = "Proceedings of IX. ECMI Conference, Kopenhagen (1996)", pages = "", publisher = "", address = "", key = "Klein1996b", abstract = "", comment = "", keywords = "Circuit simulation, transistor models, Maple.", referred = "[Klein2001a]." } @ARTICLE{Klein2000a, author = "Wolfram Klein and Andrea Walther", month = "", year = 2000, title = "Application of Techniques of Computational Differentiation to a Cooling System", journal = "Optimization Methods and Software", volume = 13, number = "", pages = "65--78", note = "Also appeared as Technical University of Dresden, preprint IOKOMO-05-1998.", key = "Klein2000a", abstract = "", comment = "", keywords = "", referred = "[Klein2001a]." } @INCOLLECTION{Klein2001a, author = "Wolfram Klein and Andreas Griewank and Andrea Walther", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Differentiation Methods for Industrial Strength Problems", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 1, pages = "3--23", note = "", publisher = "Springer", address = "New York", key = "Klein2001a", crossref = "Corliss2001b", abstract = "The importance of simulation has been growing in industrial production for many years. Because of reduced product cycles, new and more complicated computer models have to be developed more quickly. The correct description and implementation of the interaction between different components of the entire simulation model as well as the nonlinear behaviour of these components lead in many cases to the need for derivative information. In this chapter, we use software packages for automatic differentiation~(AD) in three real world simulation systems typical for a wide range of tasks that have to be solved in numerous industrial applications. We consider difficulties arising from particular aspects of the modelling such as the integration of ordinary differential equations or fixed-point iterations for the solution of equations. Furthermore, we discuss challenges caused by technical software issues such as inhomogeneous source codes written in different languages or table look-ups. Several results concerning the use of tools such as ADIFOR, Odyss{\'e}e, and ADOL-C are presented. We discuss the benefits and the difficulties of current AD techniques applied to real industrial codes. Finally, we outline possible future developments.", comment = "", keywords = "", referred = "", isbn = "" } @ARTICLE{Knoll2000a, author = "Dana A. Knoll and W. J. Rider", month = "", year = 2000, title = "A Multigrid Preconditioned {N}ewton-{K}rylov Method", journal = "SIAM J. Sci. Stat. Comput.", volume = 21, number = "", pages = "691--710", note = "", key = "Knoll2000a", abstract = "", comment = "", keywords = "", referred = "[Keyes2001a]." } @BOOK{Knuth1998a, author = "Donald E. Knuth", year = 1981, title = "The Art of Computer Programming, Vol. 2. Seminumerical Algorithms", edition = "Third", series = "", publisher = "Addison-Wesley", address = "Reading, Mass.", key = "Knuth1998a", abstract = "", comment = "", keywords = "", referred = "[Braconnier2001a].", isbn = "0--201--89684--2" } @ARTICLE{Koriva1994a, author = "Vamshi Mohan Koriva and Arthur C. {Taylor III} and Perry A. Newman and Gene W. Hou and Henry E. Jones", month = "", year = 1994, title = "An Approximately Factored Incremental Strategy for Calculating Consistent Discrete Aerodynamic Sensitivity Derivatives", journal = "Journal of Computational Physics", volume = 113, number = "", pages = "336--346", note = "", key = "Koriva1994a", abstract = "", comment = "Uses Delta update form and AF for updating flow and derivatives.", keywords = "", referred = "[Forth2001a]." } @ARTICLE{Kraft1994a, author = "D.~Kraft", month = "", year = 1994, title = "Algorithm 733: {TOMP}---{Fortran} Modules for Optimal Control Calculations", journal = "ACM Trans. Math. Software", volume = 20, number = "", pages = "262--281", note = "", key = "Kraft1994a", abstract = "", comment = "", keywords = "", referred = "[Casanova2001a]." } @BOOK{Kreinovich1998a, author = "Vladik Kreinovich and Anatoly Lakeyev and Jiri Rohn and Patrick Kahl", editor = "", year = 1998, title = "Computational Complexity and Feasibility of Data Processing and Interval Computations", series = "Applied Optimization", number = 10, note = "", publisher = "Kluwer", address = "Dordrecht, Netherlands", key = "Kreinovich1998a", abstract = "", comment = "", keywords = "", referred = "[Kearfott2001a].", isbn = 0792348656 } @INCOLLECTION{Kubota1991a, author = "Koichi Kubota", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "{PADRE2}, A {F}ortran Precompiler Yielding Error Estimates and Second Derivatives", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "251--262", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Kubota1991a", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "[Shirieav1996a].", isbn = "0--89871--284--X" } @INCOLLECTION{Kubota1996a, author = "Koichi Kubota", editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank", year = 1996, title = "{PADRE2} - {Fortran} Precompiler for Automatic Differentiation and Estimates of Rounding Error", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "367--374", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Kubota1996a", crossref = "Berz1996c", abstract = "We are developing a FORTRAN 77 precompiler, named PADRE2, that is a tool for automatic differentiation. It reads in a set of Fortran subroutine/function subprograms that computes a (vector) value of a mathematical function, and it generates another set of subprograms that computes the values of the first-order and the second-order partial derivatives of the function as well as estimates of rounding errors accumulated in the computed values of the function. One of the unique features of our tool is the calculation of estimates of rounding errors accumulated in the values of the partial derivatives computed by automatic differentiation itself. A numerical experiment shows that these estimates are useful for setting up a stopping criterion in numerical algorithms for optimization.", comment = "", keywords = "PADRE2, precompiler, estimate rounding errors, Voronoi diagram.", referred = "[Braconnier2001a], [Jerrell1996a]." } @INBOOK{Kuester1973a, author = "James L. Kuester and Joe H. Mize", editor = "", year = 1973, title = "Optimization Techniques with {F}ortran", booktitle = "", series = "", number = "", pages = "240--250", note = "", publisher = "McGraw-Hill", address = "New-York", key = "Kuester1973a", abstract = "", comment = "", keywords = "", referred = "[Souli\'e2001a]." } @BOOK{Kulisch1981a, author = "Ulrich W. Kulisch and Willard L. Miranker", year = 1981, title = "Computer Arithmetic in Theory and Practice", series = "", volume = "", note = "", publisher = "Academic Press", address = "New York", key = "Kulisch1981a", abstract = "", comment = "", keywords = "", referred = "[Berz2001a], [Fuchi1996a], [Makino2001a].", isbn = "0--12--428650--X" } @INPROCEEDINGS{Kunkel1991a, author = "Peter Kunkel", editor = "R. Seydel and F. W. Schneider and T. K{\"u}pper and H. Troger", year = 1991, title = "Augmented Systems for Generalized Turning Points", booktitle = "Proceedings of the Conference at W{\"u}rzburg, Aug. 1990, Bifurcation and Chaos: Analysis, Algorithms, Applications", series = "", number = "", pages = "231--236", note = "", publisher = "Birkh{\"a}user", address = "Basel", key = "Kunkel1991a", abstract = "", comment = "", keywords = "", referred = "[Hoefkens2001a]." } @ARTICLE{Labik1985a, author = "Stanislas Labik and Anatol Malijevski and Peter Vonka", month = "", year = 1985, title = "A Rapidly Convergent Method of Solving the {OZ} Equation", journal = "Mol.~Phys.", volume = 56, number = "", pages = "709--715", note = "", key = "Labik1985a", abstract = "", comment = "", keywords = "", referred = "[Charpentier2001a]." } @ARTICLE{Langlois1998a, author = "Philippe Langlois and Fabrice Nativel", month = "", year = 1998, title = "Reduction and Bounding of the Rounding Error in Floating Point Arithmetic", journal = "C.R. Acad. Sci. Paris, S\'erie 1", volume = 327, number = "", pages = "781--786", note = "", key = "Langlois1998a", abstract = "", comment = "", keywords = "", referred = "[Braconnier2001a]." } @ARTICLE{Langlois1999a, author = "Philippe Langlois and Fabrice Nativel", month = "", year = 1999, title = "When Automatic Linear Correction of Rounding Errors is Exact", journal = "C.R. Acad. Sci. Paris, S\'erie 1", volume = 328, number = "", pages = "543--548", note = "Erratum in 328:829, 1999.", key = "Langlois1999a", abstract = "", comment = "", keywords = "", referred = "[Braconnier2001a]." } @ARTICLE{Langlois2001a, author = "Philippe Langlois", month = "", year = 2001, title = "Automatic Linear Correction of Rounding Errors", journal = "BIT", volume = 41, number = 3, pages = "515--539", note = "", key = "Langlois2001a", abstract = "", comment = "", keywords = "", referred = "[Braconnier2001a]." } @BOOK{Langtangen1999a, author = "Hans Petter Langtangen", editor = "", year = 1999, title = "Computational Partial Differential Equations: {N}umerical Methods and {D}iffpack Programming", series = "Lecture Notes in Computational Science and Engineering", number = 2, note = "", publisher = "Springer", address = "Berlin", key = "Langtangen1999a", abstract = "", comment = "", keywords = "", referred = "[Tijskens2001a].", isbn = 3540652744 } @INCOLLECTION{Lawson1991a, author = "Charles L.~Lawson", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "Automatic Differentiation of Inverse Functions", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "87--94", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Lawson1991a", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "[Flan91a].", isbn = "0--89871--284--X" } @INCOLLECTION{Layne1991a, author = "J.~Daniel Layne", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "Applying Automatic Differentiation and Self-Validating Numerical Methods in Satellite Simulations", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "211--217", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Layne1991a", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "", isbn = "0--89871--284--X" } @PHDTHESIS{Le1999a, author = "Cong Tanh Le", month = "", year = 1999, title = "Contr\^ole optimal et transfert orbital en temps minimal", note = "", address = "Institut National Polytechnique de Toulouse, France", school = "ENSEEIHT", key = "Le1999a", abstract = "", comment = "", keywords = "", referred = "[Caillau2001a]." } @INPROCEEDINGS{LeBris2000a, author = "Claude {Le Bris}", editor = "", year = 2000, title = "Control Theory Applied to Quantum Chemistry: {S}ome Tracks", booktitle = "International Conference on Control of Systems Governed by PDEs (Nancy, March 1999)", volume = 8, pages = "77--94", note = "See \url{cermics.enpc.fr/reports/CERMICS-99-174.ps.gz}", publisher = "ESAIM PROC", address = "", key = "LeBris2000a", abstract = "", comment = "", keywords = "", referred = "[Ben-Haj-Yedder2001a]." } @ARTICLE{LeDimet1986a, author = "Fran{\c c}ois-Xavier {Le Dimet} and Olivier Talagrand", month = "", year = 1986, title = "Variational Algorithms for Analysis and Assimilation of Meteorological Observations: {T}heoretical Aspects", journal = "Tellus", volume = "38A", number = "", pages = "97--110", key = "LeDimet1986a", abstract = "", comment = "", keywords = "", referred = "[Cappelaere2001a], [Griffith1996a]." } @ARTICLE{Lee1995a, author = "Lloyd~L. Lee", month = "", year = 1995, title = "An Accurate Integral Equation Theory for Hard Spheres: {R}ole of the Zero-Separation Theorems in the Closure Relation", journal = "J.~Chem.~Phys", volume = 103, number = "", pages = "9388--9396", note = "", key = "Lee1995a", abstract = "", comment = "", keywords = "", referred = "[Charpentier2001a]." } @TECHREPORT{Lee2000a, author = "Steven L.~Lee and Alan C.~Hindmarsh and Peter N.~Brown", month = "", year = 2000, title = "User Documentation for {SensPVODE}, a Variant of {PVODE} for Sensitivity Analysis", number = "UCRL-MA-140211", note = "", address = "", institution = "Lawrence Livermore National Laboratory", key = "Lee2000a", type = "", abstract = "", comment = "", keywords = "", referred = "[Lee2001a]." } @INCOLLECTION{Lee2001a, author = "Steven L.~Lee and Paul D.~Hovland", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Sensitivity Analysis Using Parallel {ODE} Solvers and Automatic Differentiation in {C}: {SensPVODE} and {ADIC}", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 26, pages = "223--229", note = "", publisher = "Springer", address = "New York", key = "Lee2001a", crossref = "Corliss2001b", abstract = "PVODE is a high-performance ordinary differential equation solver for the types of initial value problems (IVPs) that arise in large-scale computational simulations. Often, one wants to compute sensitivities with respect to certain parameters in the IVP. We discuss the use of automatic differentiation (AD) to compute these sensitivities in the context of PVODE. Results on a simple test problem indicate that the use of AD-generated derivative code can reduce the time to solution over finite difference approximations.", comment = "Also appeared as Mathematics and Computer Science Division, Argonne National Laboratory preprint ANL/MCS-P818-0500.", keywords = "", referred = "[Abate2001a], [Carle2001a].", isbn = "" } @INPROCEEDINGS{Lemarechal1977a, author = "Claude Lemar{\'e}chal and R. Mifflin", year = 1977, title = "Nonsmooth Optimization", booktitle = "Proceedings of a {IIASA} Workshop", pages = "", publisher = "Pergamon Press", address = "Oxford", key = "Lemarechal1977a", abstract = "", comment = "", keywords = "", referred = "[Berz2001a], [Hassold1996a]." } @TECHREPORT{Li1999a, author = "Shengtai Li and Linda Petzold", month = "", year = 1999, title = "Design of New {DASPK} for Sensitivity Analysis", number = "TRCS99--28", note = "", address = "", institution = "University of California at Santa Barbara", key = "Li1999a", type = "", abstract = "", comment = "", keywords = "", referred = "[Abate2001a], [Lee2001a]." } @BOOK{Linhart1986a, author = "H. Linhart and W. Zucchini", editor = "", year = 1986, title = "Model Selection", series = "Wiley Series in Probability and Mathematical Statistics", number = "", note = "", publisher = "John Wiley and Sons, Inc.", address = "", key = "Linhart1986a", abstract = "", comment = "", keywords = "", referred = "[Huiskes2001a].", isbn = "" } @ARTICLE{Linnainmaa1983a, author = "Seppo Linnainmaa", month = "", year = 1983, title = "Error Linearization as an Effective Tool for Experimental Analysis of the Numerical Stability of Algorithms", journal = "BIT", volume = 23, number = "", pages = "346--359", note = "", key = "Linnainmaa1983a", abstract = "", comment = "", keywords = "", referred = "[Braconnier2001a]." } @BOOK{Lions1971a, author = "J. L. Lions", editor = "", year = 1971, title = "Optimal Control of Systems Governed by Partial Differential Equations", series = "", number = "", note = "", publisher = "Springer", address = "", key = "Lions1971a", abstract = "", comment = "", keywords = "", referred = "[Hascoet2001a].", isbn = "" } @BOOK{Litvin1994a, author = "Faydor L. Litvin", editor = "", year = 1994, title = "Gear Geometry and Applied Theory", series = "", number = "", note = "", publisher = "Prentice Hall", address = "Englewood Cliffs, N.~J.", key = "Litvin1994a", abstract = "", comment = "", keywords = "", referred = "[Vogel2001a].", isbn = 0132110954 } @TECHREPORT{Liu1997a, author = "M. D. Liu and A. L. Tits", month = "", year = 1997, title = "User's Guide for {ADIFFSQP} {V}ersion 0.9: {A} Utility Program that Allows the User of the {FFSQP} Constrained Nonlinear Optimization Routines to Conveniently Invoke the Computational Differentiation Preprocessor {ADIFOR} 2.0", number = "", note = "", address = "College Park, MD, USA", institution = "University of Maryland, Systems Research Center", key = "Liu1997a", type = "{T}echnical {R}eport", abstract = "", comment = "", keywords = "", referred = "[Mor\'e2001a]." } @TECHREPORT{Loebel, author = "G.~L{\"o}bel", month = "", year = "", title = "Ein Neues {P}rogrammkonzept zur {S}imulation von {D}ampferzeugern", number = "TSE3/B17", note = "", address = "", institution = "Siemens", key = "Loebel", type = "Siemens-Bericht", abstract = "", comment = "", keywords = "", referred = "[Klein2001a]." } @ARTICLE{Maar2000a, author = "Bernd Maar and Volker Schulz", month = "", year = 2000, title = "Interior Point Multigrid Methods for Topology Optimization", journal = "Struct. Optim.", volume = 19, number = 3, pages = "214--224", note = "Also appeared as IWR, University of Heidelberg Technical Report 98--57, 1998.", key = "Maar2000a", abstract = "", comment = "", keywords = "", referred = "[Haase2001a]." } @ARTICLE{Mahlke1992a, author = "S. A. Mahlke and W. Y. Chen and J. C. Gyllenhaal and W.-M. W. Hwu", month = "", year = 1992, title = "Compiler Code Transformations for Superscalar-Based High Performance Systems", journal = "Proceedings of the 1992 Conference on Supercomputing (Washington D.C.)", volume = "", number = "", pages = "808--817", note = "", key = "Mahlke1992a", abstract = "", comment = "", keywords = "", referred = "[Bodin2001a]." } @INCOLLECTION{Mahmoud1994a, author = "Kamel G. Mahmoud", editor = "B. H. V. Topping and M. Papadrakakis", year = 1994, title = "Approximations in Optimum Structural Design", booktitle = "Advanced in Structural Optimization", series = "", number = "", pages = "57--67", note = "", publisher = "Civil-Comp Press", address = "Edinburgh", key = "Mahmoud1994a", abstract = "", comment = "", keywords = "", referred = "[Haase2001a]." } @INCOLLECTION{Makino1996a, author = "Kyoko Makino and Martin Berz", editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank", year = 1996, title = "Remainder Differential Algebras and their Applications", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "63--74", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Makino1996a", crossref = "Berz1996c", abstract = "In many practical problems in which derivatives are calculated, their basic purpose is to be used in the modeling of a functional dependence, often based on a Taylor expansion to first or higher orders. While the practical computation of such derivatives is greatly facilitated and in many cases is possible only through the use of forward or reverse computational differentiation, there is usually no direct information regarding the accuracy of the functional model based on the Taylor expansion. We show how, in parallel to the accumulation of derivatives, error bounds of all functional dependencies can be carried along the computation. The additional effort is minor, and the resulting bounds are usually rather sharp, in particular at higher orders. This Remainder Differential Algebraic Method is more straightforward and can yield tighter bounds than the mere interval bounding of the Taylor remainder's $(n+1)$st order derivative obtained via forward differentiation. The method can be applied to various numerical problems: Here we focus on global optimization, where blow-up can often be substantially reduced compared with interval methods, in particular for the cases of complicated functions or many variables. This problem is at the core of many questions of nonlinear dynamics and can help facilitate a detailed, quantitative understanding.", comment = "", keywords = "Remainder Differential Algebras, Differential Algebras, error bound, interval method, high-order derivatives, Taylor polynomial, Taylor remainder, beam physics, COSY INFINITY, Fortran precompiler.", referred = "[Berz1996b], [Berz2001a], [Jerrell1996a], [Makino2001a]." } @PHDTHESIS{Makino1998a, author = "Kyoko Makino", month = "", year = 1998, title = "Rigorous Analysis of Nonlinear Motion in Particle Accelerators", note = "Also MSUCL-1093 and \url{bt.nscl.msu.edu/papers-cgi/display.pl?name=makinophd }.", address = "East Lansing, {M}ichigan, {USA}", school = "{M}ichigan {S}tate {U}niversity", key = "Makino1998a", abstract = "", comment = "", keywords = "", referred = "[Berz2001a], [Hoefkens2001a], [Makino2001a]." } @ARTICLE{Makino1999a, author = "Kyoko Makino and Martin Berz", month = "", year = 1999, title = "Efficient Control of the Dependency Problem Based on {T}aylor Model Methods", journal = "Reliable Computing", volume = 5, number = 1, pages = "3--12", note = "", key = "Makino1999a", abstract = "", comment = "", keywords = "", referred = "[Kearfott2001a], [Makino2001a]" } @INCOLLECTION{Makino2001a, author = "Kyoko Makino and Martin Berz", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "New Applications of {T}aylor Model Methods", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 43, pages = "359--364", note = "", publisher = "Springer", address = "New York", key = "Makino2001a", crossref = "Corliss2001b", abstract = "Taylor model methods unify many concepts of high-order computational differentiation with verification approaches covering the Taylor remainder term. Not only do they provide local multivariate derivatives, they also allow for highly efficient and sharp verification. We present several recent results obtained with Taylor model methods, including verified optimization, verified quadrature and verified propagation of extended domains of initial conditions through ODEs, approaches towards verified solution of DAEs and PDEs. In all cases, the methods allow the development of new numeric-analytic tools that efficiently capitalize on the availability of derivatives and sharp inclusions over extended ranges. Applications of the methods are given, including global optimization, very high-dimensional numeric quadrature, particle accelerators, and dynamics of near-earth asteroids.", comment = "", keywords = "", referred = "[Kearfott2001a].", isbn = "" } @ARTICLE{Malanowski1996a, author = "Kazimierz Malanowski and Helmut Maurer", month = "", year = 1996, title = "Sensitivity Analysis for Parametric Optimal Control Problems with Control-State Constraints", journal = "Comp. Optim. Appl.", volume = 5, number = "", pages = "253--283", note = "", key = "Malanowski1996a", abstract = "", comment = "", keywords = "", referred = "[Caillau2001a]." } @ARTICLE{Malanowski1997a, author = "Kazimierz Malanowski", month = "", year = 1997, title = "Sufficient Optimality Conditions for Optimal Control Subject to State Constraints", journal = "SIAM J. Cont. Opt.", volume = 35, number = "", pages = "205--227", note = "", key = "Malanowski1997a", abstract = "", comment = "", keywords = "", referred = "[Caillau2001a]." } @ARTICLE{Maly1996a, author = "T.~Maly and Linda Petzold", month = "", year = 1996, title = "Numerical Methods and Software for Sensitivity Analysis of Differential-Algebraic Systems", journal = "Applied Numerical Mathematics", volume = 20, number = "1-2", pages = "57--79", note = "", key = "Maly1996a", abstract = "", comment = "", keywords = "", referred = "[Lee2001a]." } @INCOLLECTION{Mancini1998a, author = "Marco Mancini", editor = "Christ{\`e}le Faure", year = 1998, title = "A Hierarchical Approach in Automatic Differentiation", booktitle = "Automatic Differentiation for Adjoint Code Generation", series = "Technical Report no. 3555", number = "", pages = "39--45", note = "", publisher = "INRIA", address = "", key = "Mancini1998a", abstract = "", comment = "", keywords = "", referred = "[Mancini2001a]." } @INCOLLECTION{Mancini2001a, author = "Marco Mancini", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "A Parallel Hierarchical Approach for Automatic Differentiation", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 27, pages = "231--236", note = "", publisher = "Springer", address = "New York", key = "Mancini2001a", crossref = "Corliss2001b", abstract = "We evaluate in parallel first-order derivatives given a sequential computer program of the function to be differentiated. Our parallel implementation of an automatic differentiation (AD) algorithm is based on a hierarchical approach. The parallel method is developed by considering as a parallel computational model a shared-memory paradigm. The performance of the derivative codes is evaluated by considering a SGI Origin 2000 and by using the OPENMP standard library. In our computational experiments, we have considered the {\em Flow in a Driven Cavity} function belonging to the MINPACK-2 test problem collection. The computational results show the performance gain of the parallel approach over both the sequential one and the stripmining technique.", comment = "", keywords = "", referred = "", isbn = "" } @ARTICLE{Marquardt1963a, author = "W. Donald Marquardt", month = "", year = 1963, title = "An Algorithm for Least Squares Estimation of Non-Linear Parameters", journal = "J. Soc. Indust. Appl. Math.", volume = 11, number = 2, pages = "413--441", note = "", key = "Marquardt1963a", abstract = "", comment = "", keywords = "", referred = "[Souli\'e2001a]." } @BOOK{Martynov1992a, author = "Georgy A. Martynov", editor = "", year = 1992, title = "Fundamental Theory of Liquids: {M}ethods of Distribution Functions", series = "", number = "", note = "", publisher = "Adam Hilger", address = "", key = "Martynov1992a", abstract = "", comment = "", keywords = "", referred = "[Charpentier2001a].", isbn = 0750300698 } @MISC{MATLAB2000a, author = "{The MathWorks}", month = "", year = 2000, title = "MATLAB 5.3.1", note = "See \url{www.mathworks.com/products/matlab}", howpublished = "", key = "MATLAB2000a", abstract = "", comment = "", keywords = "", referred = "[Keyes2001a]." } @ARTICLE{Maute1995a, author = "Kurt Maute and Ekkehard Ramm", month = "", year = 1995, title = "Adaptive Topology Optimization", journal = "Struct. Optim.", volume = 10, number = "", pages = "100--112", note = "", key = "Maute1995a", abstract = "", comment = "", keywords = "", referred = "[Haase2001a]." } @INCOLLECTION{Mazourik1991a, author = "Vladimir Mazourik", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "Integration of Automatic Differentiation into a Numerical Library for {PC}'s", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "286--293", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Mazourik1991a", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "[Jued91a].", isbn = "0--89871--284--X" } @ARTICLE{McHugh1998a, author = "P. R. {McHugh} and Dana A. Knoll and David E. Keyes", month = "", year = 1998, title = "Application of a {N}ewton-{K}rylov-{S}chwarz Algorithm to Low {M}ach Number Combustion", journal = "AIAA J.", volume = 36, number = "", pages = "290--292", note = "", key = "McHugh1998a", abstract = "", comment = "", keywords = "", referred = "[Keyes2001a]." } @INCOLLECTION{Megrey1989a, author = "B. A. Megrey", editor = "B.A. Megrey and E.F. Edward", year = 1989, title = "Review and Comparison of Age-Structured Stock Assessment Models from Theoretical and Applied Point of View", booktitle = "Mathematical Analysis of Fish Stock Dynamics", series = "", number = "", pages = "", note = "", publisher = "American Fisheries Society", address = "", key = "Megrey1989a", abstract = "", comment = "", keywords = "", referred = "[Huiskes2001a]." } @BOOK{Meyers1992a, author = "Scott Meyers", editor = "", year = 1992, title = "Effective C++: 50 Ways to Improve Your Programs and Designs", series = "", number = "", note = "", publisher = "Addison-Wesley", address = "", key = "Meyers1992a", abstract = "", comment = "", keywords = "", referred = "[Tijskens2001a].", isbn = "" } @INCOLLECTION{Michelotti1991a, author = "Leo Michelotti", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "{MXYZPTLK}: {A} {C}++ Hacker's Implementation of Automatic Differentiation", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "218--227", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Michelotti1991a", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "", isbn = "0--89871--284--X" } @ARTICLE{Miele1969a, author = "A. Miele and J. W. Cantrell", month = "", year = 1969, title = "Study on a Memory Gradient Method for the Minimization of Functions", journal = "Journal of Optimization Theory and Applications", volume = 3, number = "", pages = "459--470", key = "Miele1969a", abstract = "", comment = "", keywords = "", referred = "[Christianson2001a]." } @INCOLLECTION{Mohammadi1996a, author = "Bijan Mohammadi and Jean-Michel Mal{\'e} and Nicole Rostaing-Schmidt", editor = "Martin Berz and Christian H.~Bischof and George F.~Corliss and Andreas Griewank", year = 1996, title = "Automatic Differentiation in Direct and Reverse Modes: Application to Optimum Shapes Design in Fluid Mechanics", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "309--318", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Mohammadi1996a", crossref = "Berz1996c", abstract = "We first give a description of the Odyss{\'e}e system. Odyss{\'e}e takes as input a Fortran program and a set of variables and returns a new Fortran program computing the derivatives of the original function with respect to the given variables. Direct differentiation, producing a Jacobian matrix or a gradient vector, and reverse mode, computing the linear cotangent map, are implemented in Odyss{\'e}e. The available strategies of differentiation are presented: they lead to different computation speeds and memory requirements. We consider problems belonging to optimal shape design in aeronautics. Some implicit functional must be minimized over a set of possible shapes, under the constraint that the stationary Euler equations of the surrounding flow are verified. We describe the physical problems and the numerical methods used for solving them. We discuss the advantages and drawbacks of two different approaches in the use of Odyss{\'e}e for solving the optimization problem. These approaches are analyzed on several tes", comment = "", keywords = "Optimum shape design, computational fluid mechanics, aeronautics, Odyss{\'e}e.", referred = "[Bischof1996b], [Hascoet2001a]." } @INCOLLECTION{Monagan1996a, author = "Michael Monagan and Ren{\'e} R.~Rodoni", editor = "Martin Berz and Christian H.~Bischof and George F.~Corliss and Andreas Griewank", year = 1996, title = "Automatic Differentiation: An Implementation of the Forward and Reverse mode in {M}aple", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "353--362", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Monagan1996a", crossref = "Berz1996c", abstract = "We present a new environment for automatic differentiation in the Maple computer algebra system. Our implementation includes the reverse mode and may be applied to a wide variety of Maple procedures. Also presented is a discussion of the model of automatic differentiation used, code optimization issues, the generation of Fortran/C code, and some details of the implementation.", comment = "", keywords = "Maple, symbolic differentiation, reverse mode, code optimization, automatic code generation.", referred = "" } @BOOK{Moore1966a, author = "Ramon E. Moore", year = 1966, title = "Interval Analysis", publisher = "Prentice Hall", address = "Englewood Cliffs, N.J.", key = "Moore1966a", abstract = "Chapter ten of this book discusses the machine generation of Taylor coefficients. Basic recursion relations are presented.", comment = "German translation: {\sl Intervallanalyse,\/} translated by D. Pfaffenzeller, R. Oldenburg, M{\"u}nchen, 1968.", keywords = "boundary value problems; wrapping effect; coordinate transformation; Taylor coefficients.", referred = "[Berz2001a], [Makino2001a], [Rall1996a].", isbn = "" } @BOOK{Moore1979a, author = "Ramon E. Moore", year = 1979, title = "Methods and Applications of Interval Analysis", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Moore1979a", abstract = "Chapter 3 of this book discusses differation arithmetic as a recursive iteration. That is, for calculating Taylor coefficients.", comment = "", keywords = "operator equations; Taylor series; wrapping effect; boundary value problems.", referred = "[Berz2001a], [Kubota1996a], [Makino2001a], Rall1996a].", isbn = "0--89871--161--4" } @BOOK{Moore1988a, author = "", editor = "Ramon E. Moore", year = 1988, title = "Reliability in Computing: {T}he Role of Interval Methods in Scientific Computing", series = "", number = "", note = "", publisher = "Academic Press", address = "San Diego", key = "Moore1988a", abstract = "", comment = "", keywords = "", referred = "[Berz2001a], [Makino2001a].", isbn = "0--12--505630--3" } @MISC{Moore1998a, author = "Ramon E. Moore", month = "", year = 1998, title = "", note = "", howpublished = "Private communication", key = "Moore1998a", abstract = "", comment = "", keywords = "", referred = "[Makino2001a]." } @ARTICLE{Morita1960a, author = "T. Morita and Kazuo Hiroike", month = "", year = 1960, title = "A New Approach to the Theory of Classical Fluids", journal = "Prog.~Theor.~Phys.", volume = 23, number = "", pages = 1003, note = "", key = "Morita1960a", abstract = "", comment = "", keywords = "", referred = "[Charpentier2001a]." } @INCOLLECTION{Mor‰1977a, author = "Jorge J. Mor{\'e}", editor = "G. A. Watson", year = 1977, title = "The {L}evenberg-{M}arquardt Algorithm: {I}mplementation and Theory", booktitle = "Lecture Notes in Mathematics", series = "", number = "", pages = "105--116", note = "", publisher = "Springer Verlag", address = "Berlin", key = "Mor\'e1977a", abstract = "", comment = "", keywords = "", referred = "[Souli\'e2001a]." } @INCOLLECTION{Mor‰2001a, author = "Jorge J.~Mor{\'e}", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Automatic Differentiation Tools in Optimization Software", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 2, pages = "25--34", note = "", publisher = "Springer", address = "New York", key = "Mor\'e2001a", crossref = "Corliss2001b", abstract = "We discuss the role of automatic differentiation tools in optimization software. We emphasize issues that are important to large-scale optimization and that have proved useful in the installation of nonlinear solvers in the NEOS Server. Our discussion centers on the computation of the gradient and Hessian matrix for partially separable functions and shows that the gradient and Hessian matrix can be computed with guaranteed bounds in time and memory requirements.", comment = "", keywords = "", referred = "", isbn = "" } @BOOK{Muchnick1997a, author = "Steven S. Muchnick", editor = "", year = 1997, title = "Advanced Compiler Design Implementation", series = "", number = "", note = "", publisher = "Morgan Kaufmann Publishers", address = "San Francisco, California", key = "Muchnick1997a", abstract = "", comment = "", keywords = "", referred = "[Giering2001a].", isbn = 1558603204 } @ARTICLE{Murray1984a, author = "D. M. Murray and S. J. Yakowitz", month = "", year = 1984, title = "Differential Dynamic Programming and {N}ewton's Method for Discrete Optimal Control Problems", journal = "Journal of Optimization Theory and Applications", volume = 43, number = 3, pages = "395--414", key = "Murray1984a", abstract = "", comment = "", keywords = "", referred = "[Christianson2001a]." } @ARTICLE{Myers1995a, author = "Nathan C. Myers", month = "", year = 1995, title = "Traits: {A} New and Useful Template Technique", journal = "C++ Report", volume = "", number = "", pages = "", note = "See \url{www.cantrip.org/traits.html}", key = "Myers1995a", abstract = "", comment = "", keywords = "", referred = "[Aubert2001a]." } @ARTICLE{Mykut1971a, author = "G.~A.~Mykut and N.~Untersteiner", month = "", year = 1971, title = "Some Results from a Time Dependent Thermodynamic Model of Sea-Ice", journal = "J.~Geophys.~Res.", volume = 76, number = "", pages = "1550--1575", note = "", key = "Mykut1971a", abstract = "", comment = "", keywords = "", referred = "[Kim2001a]." } @ARTICLE{Mysak1990a, author = "L.~A.~Mysak and D.~K.~Manak and R.~F.~Marsden", month = "", year = 1990, title = "Sea-Ice Anomalies Observed in the {G}reenland and {L}abrador Seas during 1901-1984 and Their Relationship to an Interdecadal {A}rctic Climate Cycle", journal = "Climate Dyn.", volume = 5, number = "", pages = "111--133", note = "", key = "Mysak1990a", abstract = "", comment = "", keywords = "", referred = "[Kim2001a]." } @MANUAL{NAG1997a, author = "NAG", month = "", year = 1997, title = "NAG Fortran Library Manual, Mark 18", number = "", note = "", address = "Oxford", organization = "The Numerical Algorithms Group Limited", key = "NAG1997a", type = "", abstract = "", comment = "", keywords = "", referred = "[Bischof2001a]." } @MISC{NAG2001a, author = "NAG", month = "", year = 2001, title = "IRIS Explorer", note = "", howpublished = "\url{www.nag.co.uk}", key = "NAG2001a", abstract = "", comment = "", keywords = "", referred = "[Hague2001a]." } @PHDTHESIS{Naumann1999a, author = "Uwe Naumann", month = "December", year = 1999, title = "Efficient Calculation of {J}acobian Matrices by Optimized Application of the Chain Rule to Computational Graphs", note = "", address = "", school = "Technical University of Dresden", key = "Naumann1999a", abstract = "", comment = "", keywords = "", referred = "[Naumann2001a], [Tadjouddine2001a]." } @INCOLLECTION{Naumann2001a, author = "Uwe Naumann", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Elimination Techniques for Cheap {J}acobians", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 29, pages = "247--253", note = "", publisher = "Springer", address = "New York", key = "Naumann2001a", crossref = "Corliss2001b", abstract = "The generation of optimized code for evaluating the Jacobian matrix of a vector function is known to result in a remarkable speedup of three and more compared to standard methods of Automatic Differentiation in most cases. So far, this optimization has been built on the elimination of vertices in the computational graph. We show that vertex elimination in general does not lead to optimal Jacobian code. We introduce two new elimination methods and demonstrate their superiority over the vertex elimination approach.", comment = "", keywords = "", referred = "[Faure2001a], [Klein2001a].", isbn = "" } @INCOLLECTION{Navon1991a, author = "I.~Michael Navon and Xiaolei Zou", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "Application of the Adjoint Model in Meteorology", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "202--207", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Navon1991a", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "", isbn = "0--89871--284--X" } @MISC{NEOS1999a, author = "{{NEOS} {S}erver for {O}ptimization {P}roblems}", month = "", year = "", title = "", note = "See \url{www-neos.mcs.anl.gov}", howpublished = "", key = "NEOS1999a", abstract = "", comment = "", keywords = "", referred = "[Klein2001a], [Mor\'e2001a]." } @BOOK{Neumaier1990a, author = "Arnold Neumaier", year = 1990, title = "Interval Methods for Systems of Equations", series = "", number = "", publisher = "Cambridge University Press", address = "Cambridge", key = "Neumaier1990a", abstract = "", comment = "", keywords = "", referred = "[Kearfott1996a], [Kearfott2001a].", isbn = "0--521--33196--X" } @ARTICLE{Newsam1983a, author = "Garry N. Newsam and John D. Ramsdell", month = "", year = 1983, title = "Estimation of Sparse {J}acobian Matrices", journal = "SIAM J. Alg. Disc. Meth.", volume = 4, number = 3, pages = "404--417", key = "Newsam1983a", abstract = "", comment = "", keywords = "", referred = "[Geitner1996a], [Griewank2001a], [Hossain2001a]." } @ARTICLE{Noailles1998a, author = "Joseph Noailles and Cong Thanh Le", month = "", year = "Gauthier-Villars, 1998", title = "Contr\^ole en temps minimal et transfert orbital \`a faible pouss\'ee", journal = "\'Equations aux d\'eriv\'ees partielles et applications", volume = "", number = "", pages = "705--724", note = "Articles in honour of J. L. Lions for his 70th birthday.", key = "Noailles1998a", abstract = "", comment = "", keywords = "", referred = "[Caillau2001a]." } @BOOK{Nocedal1999a, author = "Jorge Nocedal and Stephen J.~Wright", editor = "", year = 1999, title = "Numerical Optimization", booktitle = "", series = "Springer Series in Operations Research", number = "", note = "", publisher = "Springer-Verlag", address = "New York", key = "Nocedal1999a", abstract = "", comment = "", keywords = "", referred = "[Abate2001a], [Haase2001a], [Keyes2001a].", isbn = 0387987932 } @MISC{NumericalObjects2000a, author = "{Numerical Objects AS}", month = "", year = "", title = "Diffpack {W}orld {W}ide {W}eb home page", note = "", howpublished = "See \url{www.nobjects.com}.", key = "NumericalObjects2000a", abstract = "", comment = "", keywords = "", referred = "[Tijskens2001a]." } @ARTICLE{Ornstein1914a, author = "L.~S.~Ornstein and F.~Zernike", month = "", year = 1914, title = "", journal = "Proc.~Acad.~Sci.~Amsterdam", volume = 17, number = "", pages = 793, note = "", key = "Ornstein1914a", abstract = "", comment = "", keywords = "", referred = "[Charpentier2001a]." } @ARTICLE{Pantelides1988a, author = "Constantinos C. Pantelides", month = "", year = 1988, title = "The Consistent Initialization of Differential-Algebraic Systems", journal = "SIAM J. Sci. Stat. Comput.", volume = 9, number = 2, pages = "213--231", key = "Pantelides1988a", abstract = "", comment = "", keywords = "", referred = "[Hofkens2001a], [Feehery1996a]." } @PHDTHESIS{Pantoja1983a, author = "J. F. A. De O. Pantoja", month = "", year = 1983, title = "Algorithms for Constrained Optimization Problems", note = "", address = "", school = "Imperial College of Science and Technology, University of London", key = "Pantoja1983a", abstract = "", comment = "", keywords = "", referred = "[Christianson2001a]." } @ARTICLE{Pantoja1988a, author = "J. F. A. De O. Pantoja", month = "", year = 1988, title = "Differential Dynamic Programming and {N}ewton's Method", journal = "Int. J. Control", volume = 47, number = 5, pages = "1539--1553", key = "Pantoja1988a", abstract = "", comment = "", keywords = "", referred = "[Christianson2001a]." } @INCOLLECTION{Park1996a, author = "Seon Ki Park and Kelvin K.~Droegemeier and Christian H.~Bischof", editor = "Martin Berz and Christian H.~Bischof and George F.~Corliss and Andreas Griewank", year = 1996, title = "Automatic Differentiation as a Tool for Sensitivity Analysis of a Convective Storm in a 3-{D} Cloud Model", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "205--214", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Park1996a", crossref = "Berz1996c", abstract = "The ADIFOR automatic differentiation tool is applied to a 3-D storm-scale meteorological model to generate a sensitivity-enhanced code capable of providing derivatives of all model output variables and related diagnostic (derived) parameters as a function of specified control parameters. The tangent linear approximation, applied to a deep convective storm by the first of its kind using a full-physics compressible model, is valid up to 50 min for a 1 \% water vapor perturbation. The result is very encouraging considering the highly nonlinear and discontinuous properties of solutions. The ADIFOR-generated code has provided valuable sensitivity information on storm dynamics. Especially, it is very efficient and useful for investigating how a perturbation inserted at earlier time propagates through the model variables at later times. However, it is computationally very expensive to apply to the variational data assimilation, especially for 3-D meteorological models, which potentially have a large number of input variables.", comment = "", keywords = "Tangent linear approximation, forward sensitivity, adjoint sensitivity, variational data assimilation, convective storm, 3-D cloud model, moist convection, supercell storm.", referred = "" } @ARTICLE{Parkinson1979a, author = "C.~L.~Parkinson and W.~M.~Washington", month = "", year = 1979, title = "A Large-Scale Numerical Model of Sea-Ice", journal = "J.~Geophys.~Res.", volume = 84, number = "", pages = "311--337", note = "", key = "Parkinson1979a", abstract = "", comment = "", keywords = "", referred = "[Kim2001a]." } @TECHREPORT{Parr2000a, author = "Terence Parr and John Lilly and Peter Wells and Ric Klaren and Mika Illouz and John Mitchell and Scott Stanchfield and Jim Coker and Monty Zukowski and Chapman Flack", month = "January", year = 2000, title = "{ANTLR} {R}eference {M}anual", number = "", note = "See \url{www.antlr.org/doc/index.html}", address = "", institution = "MageLang Institute's jGuru.com", key = "Parr2000a", type = "", abstract = "", comment = "", keywords = "", referred = "[Tadjouddine2001a]." } @BOOK{Patterson1990a, author = "David A. Patterson and John L. Hennessy", editor = "", year = 1990, title = "Computer Architecture: {A} Quantitative Approach", series = "", number = "", note = "", publisher = "Morgan Kaufmann", address = "San Mateo, CA", key = "Patterson1990a", abstract = "", comment = "", keywords = "", referred = "[Bodin2001a].", isbn = "" } @TECHREPORT{Patterson1996a, author = "Ken R. Patterson and G. D. Melvin", month = "October", year = 1996, title = "Integrated Catch at Age Analysis. {V}ersion 1.2.", number = 58, note = "", address = "HMSO Edinburgh", institution = "The Scottish Office. Agriculture, Environment and Fisheries Department.", key = "Patterson1996a", type = "Scottish Fisheries Research Report", abstract = "", comment = "", keywords = "", referred = "[Huiskes2001a]." } @ARTICLE{Pele1991a, author = "H.~W.~Pele and R.~Hempelmann and M.~Prager and M.~D.~Zeidler", month = "", year = 1991, title = "Dynamics of 18-Crown-6 Ether in Aqueous Solution Studied by Quasielastic Neutron Scattering", journal = "Berichte der Bunsen-Gesellschaft f{\"u}r physikalische Chemie", volume = 95, number = 5, pages = "592--598", note = "", key = "Pele1991a", abstract = "", comment = "", keywords = "", referred = "[Bischof2001a]." } @ARTICLE{Pichat1972a, author = "Mich{\`e}le Pichat", month = "", year = 1972, title = "Correction d'une Somme en Arithm\'etique \`a Virgule Flottante", journal = "Numer. Math.", volume = 19, number = "", pages = "400--406", note = "", key = "Pichat1972a", abstract = "", comment = "", keywords = "", referred = "[Braconnier2001a]." } @ARTICLE{Pierce1997a, author = "Niles A. Pierce and Michael B. Giles", month = "", year = 1997, title = "Peconditioned Multigrid Methods for Compressible Flow Calculations on Stretched Meshes", journal = "J. Comput. Phys.", volume = 136, number = "", pages = "425--445", note = "", key = "Pierce1997a", abstract = "", comment = "", keywords = "", referred = "[Giles2001a]." } @INBOOK{Pilbrow1990a, author = "John R. Pilbrow", editor = "", year = 1990, title = "Transition Ion Electron Paramagnetic Resonance", booktitle = "", series = "", number = "", chapter = "5.3.1 Powder Averaged Transition Probability, Formula (5,22)", pages = 222, note = "", publisher = "Clarendon {P}ress", address = "Oxford", key = "Pilbrow1990a", abstract = "", comment = "", keywords = "", referred = "[Souli\'e2001a]." } @BOOK{Pironn1982a, author = "Olivier Pironneau", editor = "", year = 1982, title = "Optimal Shape Design for Elliptic Problems", series = "", number = "", note = "", publisher = "Springer", address = "", key = "Pironn1982a", abstract = "", comment = "", keywords = "", referred = "[Hascoet2001a].", isbn = 0387120696 } @INCOLLECTION{Plassmann1990a, author = "Paul E. Plassmann", editor = "Thomas F. Coleman and Y. Li", year = 1990, title = "Sparse {J}acobian Estimation and Factorization on a Multiprocessor", booktitle = "Large-Scale Optimization", pages = "152--179", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Plassmann1990a", abstract = "", comment = "", keywords = "", referred = "[Bischof1991a], [Hossain2001a]." } @INCOLLECTION{Powell1978a, author = "Michael J. D. Powell", editor = "G. A. Watson", year = 1978, title = "A Fast Algorithm for Nonlinear Constrained Optimization Calculations", booktitle = "Numerical Analysis", series = "Lecture Notes in Mathematics", number = 630, pages = "", note = "", publisher = "Springer", address = "Berlin", key = "Powell1978a", abstract = "", comment = "", keywords = "", referred = "[Haase2001a]." } @ARTICLE{Powell1979a, author = "Michael J. D. Powell and Philippe L. Toint", month = "", year = 1979, title = "On the Estimation of Sparse {H}essian Matrices", journal = "SIAM J. Numer. Anal.", volume = 16, number = "", pages = "1060--1074", note = "", key = "Powell1979a", abstract = "", comment = "", keywords = "", referred = "[Hossain2001a], [Mor\'e2001a]." } @BOOK{Press1992b, author = "William H. Press and Saul A. Teukolsky and William T. Vetterling and Brian P. Flannery", editor = "", year = 1992, title = "Numerical {R}ecipies in {F}ortran. 2nd edn.", series = "", number = "", note = "", publisher = "Cambridge University Press", address = "Cambridge", key = "Press1992b", abstract = "", comment = "", keywords = "", referred = "[Cappelaere2001a].", isbn = "" } @TECHREPORT{Pryce1998a, author = "John D. Pryce and John K. Reid", month = "", year = 1998, title = "{ADO1}, a {F}ortran 90 code for Automatic Differentiation", number = "RAL-TR-1998-057", note = "See \url{ftp://matisa.cc.rl.ac.uk/pub/reports/prRAL98057.ps.gz}", address = "Chilton, Didcot, Oxfordshire, OX11 OQX, England", institution = "Rutherford Appleton Laboratory", key = "Pryce1998a", type = "", abstract = "", comment = "", keywords = "", referred = "[Tadjouddine2001a]." } @ARTICLE{Pryce1998b, author = "John D. Pryce", month = "", year = 1998, title = "Solving High-Index {DAE}s by {T}aylor series", journal = "Numerical Algorithms", volume = 19, number = "", pages = "195--211", note = "", key = "Pryce1998b", abstract = "", comment = "", keywords = "", referred = "[Hoefkens2001a]." } @TECHREPORT{Pryce2000a, author = "John D. Pryce", month = "March", year = 2000, title = "A Simple Structural Analysis Method for {DAE}s", number = "DoIS/TR05/00", note = "", address = "", institution = "RMCS, Cranfield University", key = "Pryce2000a", type = "", abstract = "", comment = "", keywords = "", referred = "[Hoefkens2001a]." } @INCOLLECTION{Pusch1996a, author = "Gordon D.~Pusch", editor = "Martin Berz and Christian H.~Bischof and George F.~Corliss and Andreas Griewank", year = 1996, title = "Jet Space as the Geometric Arena of Automatic Differentiation", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "53--62", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Pusch1996a", crossref = "Berz1996c", abstract = "I discuss the connection between the differential geometric concept of a {\em jet\/} and Berz's differential algebra (DA) method of automatic differentiation to arbitrarily high order with respect to arbitrarily many variables. A DA-valued object is a representation of the {\em target-space projection\/} of a jet under a particular coordinate chart. Jets generalize the coordinate-independent concept of the {\em tangent map\/} of a function to higher orders of contact. Since the tangent map unifies the concepts of derivative, tangent vector, and the tangent linear model into a single geometrical object, the geometrical framework of higher-order differentiation and its natural connections to perturbation theory and to higher-order tangent models become clear. Jets contain additional structure beyond that of DA vectors; in particular, the jet concept meshes nicely with both the ``applicative'' and ``object oriented'' programming paradigms. The jet concept may therefore provide insights to guide new implementations of automatic differentiation. In particular, jets may help to define derivatives of composite objects such as structures; they also introduce a new means of error-checking, since operations combining jets originating from different source points are undefined.", comment = "", keywords = "Jet spaces, differential geometry, coordinate-free differentiation, fiber bundles.", referred = "" } @ARTICLE{Rabitz1983a, author = "H.~Rabitz and M.~Kramer and D.~Dacol", month = "", year = 1983, title = "Sensitivity Analysis in Chemical Kinetics", journal = "Ann.~Rev.~Phys.~Chem.", volume = 34, number = "", pages = "419--461", note = "", key = "Rabitz1983a", abstract = "", comment = "", keywords = "", referred = "[Lee2001a]." } @ARTICLE{Rall1966a, author = "Louis B. Rall", month = "", year = 1966, title = "Convergence of the {N}ewton Process to Multiple Solutions", journal = "Numer. Math.", volume = 9, number = "", pages = "25--37", note = "", key = "Rall1966a", abstract = "", comment = "", keywords = "", referred = "[Braconnier2001a]." } @BOOK{Rall1981a, author = "Louis B.~Rall", year = 1981, title = "Automatic Differentiation: {T}echniques and Applications", series = "Lecture Notes in Computer Science", volume = 120, publisher = "Springer-Verlag", address = "Berlin", key = "Rall1981a", abstract = "Rall gives complete details on algorithms for the generation and differentiation of code lists for expressions. Recurrence relations for Taylor coefficients are given. Applications to ordinary differential equations, quadrature, optimization, and other problems are given.", comment = "Contains all the details about how to do automatic differentiation and surveys application to ordinary differential equations.", keywords = "automatic differentiation.", referred = "[Feehery1996a], [Kearfott1996a], [Klein1996a], [Pusch1996a], [Rall1996a].", isbn = "0--540--10861--0" } @INCOLLECTION{Rall1991a, author = "Louis B.~Rall", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "Point and Interval Differentiation Arithmetics", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "17--24", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Rall1991a", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "[Pusch1996a], [Rall1996a].", isbn = "0--89871--284--X" } @INCOLLECTION{Rall1996a, author = "Louis B.~Rall and George F.~Corliss", editor = "Martin Berz and Christian H.~Bischof and George F.~Corliss and Andreas Griewank", year = 1996, title = "An Introduction to Automatic Differentiation", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "1--17", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Rall1996a", crossref = "Berz1996c", abstract = "This paper provides a gentle introduction to the field of automatic differentiation (AD), with the goal of equipping the reader for the other papers in this book. AD is the systematic application of the familiar rules of calculus to computer programs, yielding programs for the propagation of numerical values of first, second, or higher derivatives. AD can be regarded as traversing the code list (or computational graph) in the forward mode, the reverse mode, or a combination of the two. Algorithms for numerical optimization, differential equations, and interval analysis all could use AD technology to compute the required derivatives. AD typically is implemented by using either source code transformation or operator overloading. We give examples of code for each. Finally, we outline some pitfalls of AD for naive users, and we present opportunities for future research.", comment = "Also Marquette University Department of Mathematics, Statistics, and Computer Science Technical Report no. 434, Milwaukee, Wisc., July, 1996.", keywords = "Code list, forward mode, reverse mode, source code transformation, operator overloading.", referred = "[Braconnier2001a], [Christianson1996a], [Hoefkens2001a], [Klein2001a]." } @INCOLLECTION{Ramm1994a, author = "Ekkehard Ramm and Kai-Uwe Bletzinger and Reiner Reitinger and Kurt Maute", editor = "B. H. V. Topping and M. Papadrakakis", year = 1994, title = "The Challenge of Structural Optimization", booktitle = "Advanced in Structural Optimization", series = "", number = "", pages = "27--52", note = "", publisher = "Civil-Comp Press", address = "Edinburgh", key = "Ramm1994a", abstract = "", comment = "", keywords = "", referred = "[Haase2001a]." } @ARTICLE{Ratz1995a, author = "Dietmar Ratz and Tibor Csendes", month = "", year = 1995, title = "On the Selection of Subdivision Directions in Interval Branch-and-Bound Methods for Global Optimization", journal = "J. Global Optim.", volume = 7, number = "", pages = "183--207", note = "", key = "Ratz1995a", abstract = "", comment = "", keywords = "", referred = "[Kearfott2001a]." } @ARTICLE{Reissig2000a, author = "Gunther Rei{\ss}ig and Wade S. Martinson and Paul I. Barton", month = "", year = 2000, title = "Differential-Algebraic Equations of Index 1 May Have an Arbitrarily High Structural Index", journal = "SIAM J. Sci. Comput.", volume = 21, number = 6, pages = "1987--1990 (electronic)", note = "", key = "Reissig2000a", abstract = "", comment = "", keywords = "", referred = "[Hoefkens2001a].", issn = "1095-7197" } @MISC{Rigor2000a, author = "I.~Rigor and M.~Ortmeyer", month = "", year = 2000, title = "Observations of Ice {SLP}, {SAT} and Ice Motion", note = "", howpublished = "See \url{iabp.apl.washington.edu/Summary}", key = "Rigor2000a", abstract = "", comment = "", keywords = "", referred = "[Kim2001a]." } @ARTICLE{Roe1981a, author = "Philip L. Roe", month = "", year = 1981, title = "Approximate {R}iemann Solvers, Parameter Vectors, and Difference Schemes", journal = "Journal of Computational Physics", volume = 43, number = "", pages = "357--372", note = "", key = "Roe1981a", abstract = "", comment = "", keywords = "", referred = "[Tadjouddine2001a]." } @INCOLLECTION{Rostaing-Schmidt1994a, author = "Nicole Rostaing-Schmidt and Eric Hassold", editor = "Fran{\c c}ois-Xavier {Le Dimet}", year = 1994, title = "Basic Functional Representation of Programs for Automatic Differentiation in the {O}dyss{\'e}e system", booktitle = "High Performance Computing in the Geosciences", pages = "", publisher = "Kluwer Academic Publishers", address = "Dordrecht", key = "Rostaing-Schmidt1994a", abstract = "", comment = "", keywords = "", referred = "[Goldman1996a], [Mohammadi1996a], [Pusch1996a], [Kim2001a]." } @ARTICLE{Rostaing1993a, author = "Nicole Rostaing and St{\'e}phane Dalmas and Andr{\'e} Galligo", month = "", year = 1993, title = "Automatic Differentiation in {O}dyss{\'e}e", journal = "Tellus", volume = "45A", number = "", pages = "558--568", key = "Rostaing1993a", abstract = "", comment = "", keywords = "", referred = "[Bischof1996b], [Faure1996a], [Giering1997a], [Giering2001a], [Grimm1996a], [Hassold1996a], [Klein1996a], [Mohammadi1996a], [Park1996a], [Rall1996a], [Shirieav1996a]." } @INCOLLECTION{Rothfuss1993a, author = "Ralf Rothfu{\ss} and Johanna Schaffner and Michael Zeitz", editor = "", year = 1999, title = "{R}echnergest{\"u}tzte {A}nalyse und {S}ynthese nichtlinearer {S}ysteme", booktitle = "Nichtlineare Regelungen: Methoden, Werkzeuge, Anwendungen", pages = "267---291", publisher = "VDI-Verlag", address = "", key = "Rothfuss1993a", abstract = "", comment = "", keywords = "", referred = "[R{\"o}benack2001a].", isbn = "" } @ARTICLE{Rowlinson1965a, author = "John~Shipley Rowlinson", month = "", year = 1965, title = "Self-Consistent Approximation for Molecular Distribution Functions", journal = "Mol.~Phys.", volume = 9, number = "", pages = "217-227", note = "", key = "Rowlinson1965a", abstract = "", comment = "", keywords = "", referred = "[Charpentier2001a]." } @ARTICLE{R÷benack2000a, author = "Klaus R{\"o}benack and Kurt J. Reinschke", year = 2000, title = "{R}eglerentwurf mit {H}ilfe des {A}utomatischen {D}ifferenzierens", journal = "Automatisierungstechnik", volume = 48, number = 2, pages = "60--66", key = "R{\"o}benack2000a", abstract = "", comment = "", keywords = "", referred = "[R{\"o}benack2001a]." } @INCOLLECTION{R÷benack2001a, author = "Klaus R{\"o}benack and Kurt J.~Reinschke", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Nonlinear Observer Design Using Automatic Differentiation", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 15, pages = "137--142", note = "", publisher = "Springer", address = "New York", key = "R{\"o}benack2001a", crossref = "Corliss2001b", abstract = "State feedback controllers are widely used in real-world applications. These controllers require the values of the state of the plant to be controlled. An observer can provide these values. For nonlinear systems there are some observer design methods which are based on differential geometric or differential algebraic concepts. The application to non-trivial systems is limited due to a burden of symbolic computations involved. The authors propose an observer design method using automatic differentiation.", comment = "", keywords = "", referred = "", isbn = "" } @INCOLLECTION{Saarinen1991a, author = "Sirpa Saarinen and Randall Bramley and George Cybenko", editor = "Andreas Griewank and George F. Corliss", year = 1991, title = "Neural Networks, Backpropagation, and Automatic Differentiation", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "31--42", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Saarinen1991a", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "[Juedes1996a]." } @BOOK{Saltelli2000a, editor = "Andrea Saltelli and Karen Chan and Evelyn Marian Scott", year = 2000, title = "Sensitivity Analysis", series = "", volume = "", publisher = "Wiley", address = "", key = "Saltelli2000a", abstract = "", comment = "", keywords = "", referred = "[Klein2001a].", isbn = 0471998923 } @INCOLLECTION{Schaffner1999a, author = "Johanna Schaffner and Michael Zeitz", editor = "Henk Hijmeijer and Thor I. Fossen", year = 1999, title = "Variants of Nonlinear Normal Form Observer Design", booktitle = "New Direction in Nonlinear Observer Design", series = "Number 244 in Lecture Notes in Control and Information Science", number = "", pages = "161--180", publisher = "Springer", address = "Berlin", key = "Schaffner1999a", abstract = "", comment = "", keywords = "", referred = "[R{\"o}benack2001a].", isbn = "" } @BOOK{Seber1989a, author = "G. A. F. Seber and C. J. Wild", editor = "", year = 1989, title = "Nonlinear Regresssion", series = "Wiley Series in Probability and Mathematical Statistics", number = "", note = "", publisher = "John Wiley and Sons, Inc.", address = "New York", key = "Seber1989a", abstract = "", comment = "", keywords = "", referred = "[Huiskes2001a].", isbn = "" } @BOOK{Seidelmann1992a, author = "", editor = "P. K. Seidelmann", year = 1992, title = "Explanatory Supplement to the Astronomical Almanac", series = "", number = "", note = "", publisher = "University Science Books", address = "Mill Valley, California", key = "Seidelmann1992a", abstract = "", comment = "", keywords = "", referred = "[Makino2001a].", isbn = "" } @ARTICLE{Semtner1976a, author = "A.~J.~{Semtner, Jr.}", month = "", year = 1976, title = "A Model for the Thermodyanmic Growth of Sea-Ice in Numerical Investigation of Climate", journal = "J.~Phys.~Oceanogr.", volume = 6, number = "", pages = "379--389", note = "", key = "Semtner1976a", abstract = "", comment = "", keywords = "", referred = "[Kim2001a]." } @PHDTHESIS{Sevin1999a, author = "C. Sevin", month = "", year = 1999, title = "Optimisation de formes en m\'ecanique des fluides num\'erique", note = "", address = "", school = "Universit\'e Pierre et Marie Curie", key = "Sevin1999a", abstract = "", comment = "", keywords = "", referred = "[Hascoet2001a]." } @BOOK{Seydel1991a, author = "", editor = "R. Seydel and F. W. Schneider and T. K{\"u}pper and H. Troger", year = 1991, title = "Proceedings of the Conference at W{\"u}rzburg, Aug. 1990, Bifurcation and Chaos: Analysis, Algorithms, Applications", series = "", number = "", note = "", publisher = "Birkh{\"a}user", address = "Basel", key = "Seydel1991a", abstract = "", comment = "", keywords = "", referred = "[Hoefkens2001a].", isbn = "" } @INCOLLECTION{Shah1991a, author = "Piyush Shah", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "Application of Adjoint Equations to Estimation of Parameters in Distributed Dynamic Systems", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "181--190", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Shah1991a", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "", isbn = "0--89871--284--X" } @INCOLLECTION{Shamseddine1996a, author = "Khodr Shamseddine and Martin Berz", editor = "Martin Berz and Christian H.~Bischof and George F.~Corliss and Andreas Griewank", year = 1996, title = "Exception Handling in Derivative Computation with Nonarchimedean Calculus", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "37--51", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Shamseddine1996a", crossref = "Berz1996c", abstract = "While conventional computational differentiation based on the forward or reverse modes allows highly accurate computation of derivatives, there are situations where these modes fail to produce the values of derivatives, although the underlying function is differentiable. Typical examples of this phenomenon are connected to the occurrence of branch points in coding as in IF-ELSE structures as well as the occurrence of some non-differentiable parts that do not affect the differentiability of the end result. We show that based on ideas of nonarchimedean calculus on Levi-Civita fields, these problems can be avoided. It is possible to rigorously decide whether a function is differentiable or not at any given point, and if it is, to determine its derivatives to any order, even if the coding exhibits branch points or non-differentiable pieces. We give details of an implementation of the method and examples for its use for typical pathological problems.", comment = "", keywords = "Exception handling, nonarchimedean calculus, nonarchimedean field, Heaviside function, smoothness properties of computer functions, standard form of computer functions, derivatives are differential quotients, differentiability of computer functions, COSY INFINITY.", referred = "[Berz1996a], [Berz2001a], [Pusch1996a]." } @INCOLLECTION{Shamseddine2000a, author = "Khodr Shamseddine and Martin Berz", month = "", year = 2000, title = "Convergence on the {L}evi-{C}ivita Field and Study of Power Series", booktitle = "Proc. Sixth International Conference on Nonarchimedean Analysis", volume = "", number = "", pages = "283--299", note = "", publisher = "Marcel Dekker", address = "New York", key = "Shamseddine2000a", abstract = "", comment = "", keywords = "", referred = "[Berz2001a].", isbn = "0-8247-0611-0" } @ARTICLE{Sherman1996a, author = "L. L.~Sherman and Arthur C. {Taylor III} and Larry L. Green and Perry A. Newman and Gene W. Hou and Vamshi Mohan Korivi", month = "", year = 1996, title = "First- and Second-Order Aerodynamic Sensitivity Derivatives via Automatic Differentiation with Incremental Iterative Methods", journal = "J. Comput. Phys.", volume = 129, number = 2, pages = "307--331", note = "", key = "Sherman1996a", abstract = "", comment = "", keywords = "", referred = "[Giles2001a], [Lee2001a]." } @TECHREPORT{Shestakov2000a, author = "A. Shestakov and J. Milovich", month = "", year = 2000, title = "Applications of Pseudo-transient Continuation and {N}ewton-{K}rylov Methods fo the {P}oisson-{B}oltzmann and Radiation Diffusion Equations", number = "UCRL--JC--139339", note = "", address = "", institution = "Lawrence Livermore National Laboratory", key = "Shestakov2000a", type = "", abstract = "", comment = "", keywords = "", referred = "[Keyes2001a]." } @INPROCEEDINGS{Sheveleva1995a, author = "G.~Sheveleva", editor = "", year = 1995, title = "Mathematical Simulation of Spiral Bevel Gear Production and Meshing Processes with Contact and Bending Stresses", booktitle = "Proc. {IX}. World Congr. {IFToMM}", series = "", volume = 1, number = "", pages = "509--513", note = "", publisher = "", address = "", key = "Sheveleva1995a", abstract = "", comment = "", keywords = "", referred = "[Vogel2001a]." } @INCOLLECTION{Shiriaev1996a, author = "Dmitri Shiriaev", editor = "Martin Berz and Christian H.~Bischof and George F.~Corliss and Andreas Griewank", year = 1996, title = "{ADOL--F} Automatic Differentiation of {F}ortran Codes", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "375--384", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Shiriaev1996a", crossref = "Berz1996c", abstract = "The package ADOL--F is a Fortran 90 interface to the ADOL--C library and facilitates the evaluation of first and higher derivatives of vector functions that are defined by computer programs written in Fortran 90/77. The numerical values of derivative vectors are obtained free of truncation errors at a small multiple of the run time and randomly accessed memory of the given function evaluation program. Fortran 90 allows operator overloading (like C$++$) but lacks constructor/destructor operators for user-defined types. Therefore, we employ a more sophisticated scheme for the management of active temporary variables than does ADOL--C. The derivative calculations involve a possibly substantial (but always predictable) amount of data accessed strictly sequentially and therefore automatically paged out to external files.", comment = "", keywords = "Fortran, forward mode, reverse mode, ADOL--C, ADOL--F, Taylor coefficients, overloading.", referred = "[Klein1996a], [Klein2001a]." } @PHDTHESIS{Skrobanski1986a, author = "J. J. Skrobanski", month = "", year = 1986, title = "Optimization Subject to Nonlinear Constraints", note = "", address = "", school = "London University", key = "Skrobanski1986a", abstract = "", comment = "", keywords = "", referred = "[Forth2001a]." } @ARTICLE{Smith1995a, author = "J. E. Smith and G. Sohi", month = "", year = 1995, title = "The Microarchitecture of Superscalar Processors", journal = "Proceedings of the IEEE", volume = "", number = "", pages = "", note = "", key = "Smith1995a", abstract = "", comment = "", keywords = "", referred = "[Bodin2001a]." } @BOOK{Smith1996a, author = "Barry F.~Smith and Petter Bj{\o}rstad and William D.~Gropp", editor = "", year = 1996, title = "Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations", series = "", number = "", note = "", publisher = "Cambridge University Press", address = "Cambridge", key = "Smith1996a", abstract = "", comment = "", keywords = "", referred = "[Keyes2001a], [Griewank2001a].", isbn = "052149589X" } @BOOK{Snir1995a, author = "Marc Snir and Steve W.~Otto and Steven Huss-Lederman and David W.~Walker and Jack Dongarra", editor = "", year = 1995, title = "{MPI}: The Complete Reference", series = "", number = "", note = "", publisher = "MIT Press", address = "", key = "Snir1995a", abstract = "", comment = "", keywords = "", referred = "[Carle2001a].", isbn = "" } @ARTICLE{Souli‰1989a, author = "Edgar J. Souli{\'e} and Pierre C. Lesieur", month = "", year = 1989, title = "Quantitative Analysis of the Electron Paramagnetic Resonance Spectrum of a Uranium ({III}) Compound", journal = "J. Chem. Soc. Faraday Trans. I", volume = 85, number = 12, pages = "4053--4062", note = "", key = "Souli\'e1989a", abstract = "", comment = "", keywords = "", referred = "[Souli\'e2001a]." } @INCOLLECTION{Souli‰1991a, author = "Edgar J.~Souli{\'e}", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "User's Experience with {F}ortran Precompilers for Least Squares Optimization Problems", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "297--306", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Souli\'e1991a", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "[Garc91a].", isbn = "0--89871--284--X" } @INCOLLECTION{Souli‰2001a, author = "Edgar J. Souli{\'e} and Christ{\`e}le Faure and Th{\'e}o Berclaz and Michel Geoffroy", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Electron Paramagnetic Resonance, Optimization and Automatic Differentiation", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 10, pages = "99--106", note = "", publisher = "Springer", address = "New York", key = "Souli\'e2001a", crossref = "Corliss2001b", abstract = "This paper describes an optimization problem applied to electron paramagnetic resonance spectroscopy. Levenberg-Marquardt fails to converge using a divided differences Jacobian approximation in single precision, while it succeeds using Odyss{\'e}e-generated forward mode Jacobian values. In double precision, the optimizer returns a smaller ``minimum'' objective function with AD compared to DD in 46\% more CPU time.", comment = "", keywords = "", referred = "[Klein2001a].", isbn = "" } @PHDTHESIS{Speelpenning1980a, author = "Bert Speelpenning", month = "January", year = 1980, title = "Compiling Fast Partial Derivatives of Functions Given by Algorithms", address = "Urbana-Champaign, Ill.", school = "Department of Computer Science, University of Illinois at Urbana-Champaign", key = "Speelpenning1980a", abstract = "This is the author's doctoral thesis. It starts by comparing previous work in the area of symbolic differentiation of algorithms. Specifically it considers the work of Warner in 1975, Joss in 1976 and Kedem in 1977. The conclusions reached in this discussion are that the work by Joss is the best in terms of improvement. The author proceeds to describe how Joss' work can be improved in terms of speed, accuracy and space. A package, Jake, is described which is a compiler that takes a Fortran 66 input definition of a function. This input is limited in that only one subroutine can be specified, and that certain Fortran 66 statements are disallowed. Jake is instructed on how to perform its task by directives within the subroutine. Timing results are provided on the performance of the code produced by Jake over those where finite differencing is used.", comment = "Char -- good stuff", keywords = "point algorithm; precompiler; numerical results.", referred = "[Monagan1996a], [Rall1996a]." } @BOOK{Stadtfeld1993a, author = "Hermann J. Stadtfeld", editor = "", year = 1993, title = "Handbook of Bevel and Hypoid Gears", series = "", number = "", note = "", publisher = "Rochester Institute of Technology", address = "", key = "Stadtfeld1993a", abstract = "", comment = "", keywords = "", referred = "[Vogel2001a].", isbn = "" } @ARTICLE{Stangl1999a, author = "Christoph Stangl", month = "", year = 1999, title = "Optimal Sizing for a Class of Nonlinearly Elastic Materials", journal = "SIAM J. Optim.", volume = 9, number = 2, pages = "414--443", note = "", key = "Stangl1999a", abstract = "", comment = "", keywords = "", referred = "[Haase2001a]." } @TECHREPORT{Steihaug1997a, author = "Trond Steihaug and A.K.M.~Shahadat Hossain", month = "", year = 1997, title = "Graph Coloring and the Estimation of Sparse {J}acobian Matrices with Segmented Columns", number = 72, note = "", address = "", institution = "Department of Informatics, University of Bergen", key = "Steihaug1997a", type = "{T}echnical {R}eport", abstract = "", comment = "", keywords = "", referred = "[Hossain2001a]." } @INCOLLECTION{Tadjouddine2001a, author = "Mohamed Tadjouddine and Shaun A.~Forth and John D.~Pryce", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "{AD} Tools and Prospects for Optimal {AD} in {CFD} Flux {J}acobian Calculations", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 30, pages = "255--261", note = "", publisher = "Springer", address = "New York", key = "Tadjouddine2001a", crossref = "Corliss2001b", abstract = "We consider the problem of linearising the short (approximately $100$ lines of) code that defines the numerical fluxes of mass, energy and momentum across a cell face in a finite volume compressible flow calculation. Typical of such formulations is the numerical flux due to Roe, widely used in the numerical approximation of flow fields containing moderate to strong shocks. Roe's flux takes as input $10$ variables describing the flow either side of a cell face and returns as output the $5$ variables for the numerical flux. We present results concerning the efficiency of derivative calculations for Roe's flux using several currently available AD tools. We also present preliminary work on deriving near optimal differentiated code using the node elimination approach. We show that such techniques, within a source transformation approach, will yield substantial gains for application code such as the Roe flux.", comment = "", keywords = "", referred = "[Haase2001a].", isbn = "" } @INCOLLECTION{Talagrand1991a, author = "Oliver Talagrand", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "The Use of Adjoint Equations in Numerical Modelling of the Atmospheric Circulation", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "169--180", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Talagrand1991a", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "[Chavent1996a], [Giering1997a], [Goldman1996a], [Hascoet2001a], [Klein2001a], [Walther2001a].", isbn = "0--89871--284--X" } @INCOLLECTION{Tesfatsion1991a, author = "Leigh Tesfatsion", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "Automatic Evaluation of Higher-Order Partial Derivatives for Nonlocal Sensitivity Analysis", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "157--165", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Tesfatsion1991a", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "[Dixo91a], [Jued91a].", isbn = "0--89871--284--X" } @INCOLLECTION{Thacker1991a, author = "William Carlisle Thacker", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "Automatic Differentiation from an Oceanographer's Perspective", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "191--201", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Thacker1991a", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "[Giering1997a], [Goldman1996a].", isbn = "0--89871--284--X" } @INCOLLECTION{Thames1991a, author = "Joseph M.~Thames", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "Synthetic Calculus: {A} Paradigm for Mathematical Program Synthesis", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "263--272", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Thames1991a", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "[Jued91a].", isbn = "0--89871--284--X" } @INPROCEEDINGS{Tijskens1992a, author = "Engelbert Tijskens and Wim Schoenmaker and Karin {De Meyer}", editor = "", year = 1992, title = "Automatic Numerical Evaluation of Derivatives and its Use in Device Simulators", booktitle = "IEEE Workshop on Numerical Modelling of Processes and Devices for Integrated Circuits, NUPAD IV", series = "", number = "", pages = "251--254", note = "", publisher = "IEEE", address = "", key = "Tijskens1992a", abstract = "", comment = "", keywords = "", referred = "[Tijskens2001a]." } @ARTICLE{Tijskens2000a, author = "Engelbert Tijskens and Dirk Roose and Herman Ramon and Josse {De Baerdemaeker}", month = "", year = "submitted", title = "Automatic Differentiation for Nonlinear Partial Differential Equations: {A}n Efficient Operator Overloading Approach", journal = "Numerical Algorithms", volume = "", number = "", pages = "", note = "", key = "Tijskens2000a", abstract = "", comment = "", keywords = "", referred = "[Tijskens2001a]." } @ARTICLE{Tijskens2000b, author = "Engelbert Tijskens and Dirk Roose and Herman Ramon and Josse {De Baerdemaeker}", month = "", year = "submitted", title = "Efficient Solution of Nonlinear Partial Differential Equations by Integrating Automatic Differentiation", journal = "International Journal for Numerical Methods in Engineering", volume = "", number = "", pages = "", note = "", key = "Tijskens2000b", abstract = "", comment = "", keywords = "", referred = "[Tijskens2001a]." } @INCOLLECTION{Tijskens2001a, author = "Engelbert Tijskens and Herman Ramon and Josse {De Baerdemaeker}", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Efficient Operator Overloading {AD} for Solving Nonlinear {PDEs}", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 19, pages = "167--172", note = "", publisher = "Springer", address = "New York", key = "Tijskens2001a", crossref = "Corliss2001b", abstract = "By employing automatic differentiation (AD), solvers for nonlinear systems of PDEs can be developed which relieve the user from the extra work of linearising a nonlinear PDE system and at the same time improve performance. This is achieved by extending common AD techniques using operator overloading to take advantage of the fact that in a FEM/FD/FV framework, a limited number of functions and their partial derivatives with respect to the unknowns have to be evaluated many times. The extension is implemented in C++ for both forward and reverse modes, and compared to hand coded evaluation of derivatives and two state-of-the-art AD implementations, ADIC~\cite{Bischof1997a} and ADOL-C~\cite{Griewank1996b,Griewank1996c}. An application is discussed which dramatically reduces the cost of solver development.", comment = "", keywords = "", referred = "[Klein2001a].", isbn = "" } @ARTICLE{Tolsma2000a, author = "John E.~Tolsma and Paul I.~Barton", year = 2000, title = "{DAEPACK} An Open Modeling Environment for Legacy Models", journal = "Industrial \& Engineering Chemistry Research", volume = 39, number = 6, pages = "1826--1839", key = "Tolsma2000a" } @INCOLLECTION{Utke1996a, author = "Jean Utke", editor = "Martin Berz and Christian H.~Bischof and George F.~Corliss and Andreas Griewank", year = 1996, title = "Efficient {N}ewton Steps without {J}acobians", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "253--264", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Utke1996a", crossref = "Berz1996c", abstract = "The computation of Newton steps ({\bf NS}) is a common subproblem in iterative numerical algorithms. The usual approach requires the calculation of the Jacobian and then the solution of a linear system. The automatic differentiation (AD) technique provides an efficient way to compute a Jacobian, in particular if it has a comparatively stable sparsity structure. In the more general case where Jacobians are dense or have a changing sparsity structure, the efficiency advantages of AD cannot be fully exploited by the usual approach. Because we actually need only the Newton step, not the Jacobian matrix, we introduce an AD method that generally avoids the accumulation of the Jacobian. To this end we perform not only the known node elimination steps on the computational graph but also arc elimination steps. This can reduce the complexity that is measured by the fill-in and makes the computation of Newton steps more efficient. The outline of the method to be introduced were first proposed by Griewank in 1990. Here we show extensions and certain refinements that make the method applicable in practical situations.", comment = "", keywords = "Newton steps, arc elimination, Markovitz criterion, fill-in.", referred = "" } @BOOK{vanderSnepscheut1993a, author = "J.~{van der Snepscheut}", editor = "", year = 1993, title = "What Computing Is All About", series = "Texts and Monographs in Computer Science, Suppl.~2", number = "", note = "", publisher = "Springer Verlag", address = "Berlin", key = "vanderSnepscheut1993a", abstract = "", comment = "", keywords = "", referred = "[Walther2001a].", isbn = "" } @BOOK{VanHentenryck1997a, author = "Pascal {Van Hentenryck} and Laurent Michel and Yves Deville", editor = "", year = 1997, title = "Numerica: A Modeling Language for Global Optimization", number = "", note = "", publisher = "MIT Press", address = "Cambridge, Mass.", key = "VanHentenryck1997a", abstract = "", comment = "", keywords = "", referred = "[Kearfott2001a].", isbn = 0262720272 } @BOOK{VanLaarhoven1988a, author = "P. {Van Laarhoven} and E. Aarts", editor = "", year = 1988, title = "Simulated Annealing: Theory and Applications", series = "", number = "", note = "", publisher = "Reidel", address = "Dordrecht", key = "VanLaarhoven1988a", abstract = "", comment = "", keywords = "", referred = "[Naumann2001a].", isbn = "" } @ARTICLE{Veldhuizen1996b, author = "Todd Veldhuizen and Kumaraswamy Ponnambala", month = "", year = 1996, title = "Linear Algebra with {C}++ Template Metaprograms. {R}apid Linear Algebra Is Just One Use", journal = "Dr. Dobb's Journal", volume = "", number = "", pages = "", note = "See \url{www.ddj.com/ddj/1996/1996.08/veld.htm}", key = "Veldhuizen1996b", abstract = "", comment = "", keywords = "", referred = "[Aubert2001a]." } @MISC{Veldhuizen1998a, author = "Todd Veldhuizen", month = "", year = 1998, title = "Techniques for Scientific {C}++", note = "See \url{www.oonumerics.org/blitz/papers}", howpublished = "", key = "Veldhuizen1998a", abstract = "", comment = "", keywords = "", referred = "[Aubert2001a]." } @PHDTHESIS{Verma1998a, author = "Arun Verma", month = "", year = 1998, title = "Structured Automatic Differentiation", note = "", address = "Ithaca, NY", school = "Cornell University Department of Computer Science", key = "Verma1998a", abstract = "", comment = "", keywords = "", referred = "[Mancini2001a]." } @TECHREPORT{Vogel1997a, author = "Olaf Vogel and Ulf Hutschenreiter", month = "", year = 1997, title = "{B}erechnungen zur {K}ontaktgeometrie beim {E}ingriff bogenverzahnter {K}egelr{\"a}der und {H}ypoidr{\"a}der", number = "03-1997", note = "", address = "", institution = "Technical University of Dresden, Institute of Scientific Computing and Institute of Geometry", key = "Vogel1997a", type = "IOKOMO", abstract = "", comment = "", keywords = "", referred = "[Vogel2001a]." } @ARTICLE{Vogel2000a, author = "Olaf Vogel and Andreas Griewank and Gert B{\"a}r", month = "", year = "submitted", title = "Direct Gear Tooth Contact Analysis for Hypoid Bevel Gears", journal = "Computer Methods in Applied Mechanics and Engineering", volume = "", number = "", pages = "", key = "Vogel2000a", abstract = "", comment = "", keywords = "", referred = "[Vogel2001a]." } @INCOLLECTION{Vogel2001a, author = "Olaf Vogel", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "Accurate Gear Tooth Contact Determination and Sensitivity Computation for Hypoid Bevel Gears", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 23, pages = "197--204", note = "", publisher = "Springer", address = "New York", key = "Vogel2001a", crossref = "Corliss2001b", abstract = "We investigate a new method for gear tooth contact analysis based on a mathematical model of the generating process. The approach allows the computation of the paths of contact as the solution set of a nonlinear operator equation using a minimally augmented defining system for certain first order singularities. As a byproduct we obtain curvature properties of the gear tooth flanks, the reduced curvatures at the contact points, as well as the boundaries of the paths of contact in a convenient way. Using automatic differentiation, all the geometric quantities are computable with the machine accuracy of the computer. For the first time, we provide analytical sensitivities of the determined contact properties with respect to arbitrary machine tool settings such as additional motion parameters. Thus the systematic optimization of the gear tooth contact as well as the evaluation of the impact of perturbations on the contact pattern become available in a straightforward fashion. In order to obtain the desired sensitivity information, we compute derivative tensors of an implicit function up to order three using the software tool ADOL-C.", comment = "", keywords = "", referred = "", isbn = "" } @ARTICLE{Vompe1994a, author = "A.~G.~Vompe and G.~A.~Martynov", month = "", year = 1994, title = "The Bridge Function Expansion and the Self-Consistency Problem of the {O}rnstein-{Z}ernike Equation Solution", journal = "J.~Chem.~Phys", volume = 100, number = "", pages = "5249-5258", note = "", key = "Vompe1994a", abstract = "", comment = "", keywords = "", referred = "[Charpentier2001a]." } @PHDTHESIS{Walther1999a, author = "Andrea Walther", month = "", year = 1999, title = "Program Reversal Schedules for Single- and Multi-processor Machines", note = "", address = "Germany", school = "Institute of Scientific Computing, Technical University Dresden", key = "Walther1999a", abstract = "", comment = "", keywords = "", referred = "[Walther2001a]." } @ARTICLE{Walther2000a, author = "Andrea Walther and Andreas Griewank and Olaf Vogel", editor = "", year = 2000, title = "Higher Derivative Tensors from Univariate {T}aylor Series with Comparison to {M}aple on an Engineering Problem", booktitle = "Proceedings GAMM99 Annual Meeting, Metz", series = "Z.~Angew.~Math.~Mech.", journal = "Z. Angew. Math. Mech.", volume = 80, number = 3, pages = "813--814", note = "Proceedings GAMM99 Annual Meeting, Metz.", publisher = "", address = "", key = "Walther2000a", abstract = "", comment = "", keywords = "", referred = "[Vogel2001a]." } @TECHREPORT{Walther2000b, author = "Andrea Walther", month = "", year = 2000, title = "Program Reversals for Evolutions with Non-Uniform Step Costs", number = "", note = "", address = "", institution = "Technical University of Dresden", key = "Walther2000b", type = "Preprint {IOKOMO}-2000", abstract = "", comment = "", keywords = "", referred = "[Walther2001a]." } @INCOLLECTION{Walther2001a, author = "Andrea Walther and Andreas Griewank", editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent Hasco{\"e}t and Uwe Naumann", year = 2001, title = "New Results on Program Reversals", booktitle = "Automatic Differentiation: From Simulation to Optimization", series = "Computer and Information Science", number = "", chapter = 28, pages = "237--243", note = "", publisher = "Springer", address = "New York", key = "Walther2001a", crossref = "Corliss2001b", abstract = "For adjoint calculations, parameter estimation, and similar purposes, one may need to produce all quantities calculated during the execution of a computer program in reverse order. The simplest possible approach is to record a complete execution log and then to read it backwards. This may require massive amounts of storage. Instead one may generate the execution log piecewise by restarting the ``forward'' calculation repeatedly from suitably placed checkpoints. For such program execution reversals we present parallel reversal schedules that are provably optimal with regards to the number of concurrent processes and the total amount of memory required.", comment = "", keywords = "", referred = "[Klein2001a],", isbn = "" } @ARTICLE{Weeks1971a, author = "John~D. Weeks and David Chandler and Hans C. Andersen", month = "", year = 1971, title = "Role of Repulsive Forces in Determining the Equilibrium Structure of Simple Liquids", journal = "J.~Chem.~Phys", volume = 54, number = "", pages = "5237-5247", note = "", key = "Weeks1971a", abstract = "", comment = "", keywords = "", referred = "[Charpentier2001a]." } @ARTICLE{Wengert1964a, author = "R. E. Wengert", year = 1964, title = "A Simple Automatic Derivative Evaluation Program", journal = "Comm. ACM", volume = 7, number = 8, pages = "463--464", publisher = "", key = "Wengert1964a", abstract = "A procedure for automatic evaluation of total and partial derivatives of arbitrary algebraic functions is presented. The numerical values of derivatives are computed without developing analytic expressions for the derivatives. The function is decomposed into a sequence of elementary expressions A library is provided for differentiating of elementary functions.", comment = "", keywords = "point algorithm; differentiation arithmetic; computer program.", referred = "[Casanova2001a], [Rall1996a]." } @ARTICLE{Wexler1987a, author = "Anthony S. Wexler", year = 1987, title = "Automatic Evaluation of Derivatives", journal = "Applied Mathematics and Computation", volume = 24, number = "", pages = "19--46", key = "Wexler1987a", abstract = "This is an implementation of Wengbert's automatic differentiation method, see [Weng64a], which uses dynamic memory allocation.", comment = "", keywords = "differentiation arithmetic; computer program.", referred = "[Neid1989a]; [Tesf1991a], [Tijskens2001a]." } @TECHREPORT{Whaley1998a, author = "R. Clint Whaley and Jack J. Dongarra", month = "", year = 1998, title = "Automatically Tuned Linear Algebra Software", number = "", note = "", address = "Knoxville", institution = "Department of Computer Sciences, University of Tennessee", key = "Whaley1998a", type = "", abstract = "", comment = "", keywords = "", referred = "[Aubert2001a]." } @TECHREPORT{Whaley2000a, author = "R. Clint Whaley and Antoine Petitet and Jack J. Dongarra", month = "September", year = 2000, title = "Automated Empirical Optimization of Software and the {ATLAS} Project", number = "", note = "See \url{www.netlib.org/atlas}", address = "", institution = "Department of Computer Sciences, University of TenneSsee", key = "Whaley2000a", type = "", abstract = "", comment = "", keywords = "", referred = "[Bodin2001a]." } @ARTICLE{Wilkinson1986a, author = "James H. Wilkinson", month = "", year = 1986, title = "Error Analysis Revisited", journal = "IMA Bulletin", volume = 22, number = "11/12", pages = "192--200", note = "", key = "Wilkinson1986a", abstract = "", comment = "", keywords = "", referred = "[Braconnier2001a]." } @ARTICLE{Wolf1991a, author = "M. E. Wolf and M. S. Lam", month = "", year = 1991, title = "A Data Locality Optimization Algorithm", journal = "Proceedings of the SIGPLAN Conference on Programming Language Design and Implementation (PLDI)", volume = "", number = "", pages = "30--44", note = "", key = "Wolf1991a", abstract = "", comment = "", keywords = "", referred = "[Bodin2001a]." } @INCOLLECTION{Worley1991a, author = "Brian Worley", editor = "Andreas Griewank and George F.~Corliss", year = 1991, title = "Experience with the Forward and Reverse Mode of {GRESS} in Contaminant Transport Modeling and Other Applications", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", pages = "307--315", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Worley1991a", crossref = "Griewank1991e", abstract = "", comment = "", keywords = "", referred = "", isbn = "0--89871--284--X" } @INCOLLECTION{Yang1996a, author = "Wenhong Yang and George Corliss", editor = "Martin Berz and Christian H.~Bischof and George F.~Corliss and Andreas Griewank", year = 1996, title = "Bibliography of Computational Differentiation", booktitle = "Computational Differentiation: Techniques, Applications, and Tools", pages = "393--418", publisher = "SIAM", address = "Philadelphia, Penn.", key = "Yang1996a", crossref = "Berz1996c", abstract = "", comment = "Also Marquette University Department of Mathematics, Statistics, and Computer Science Technical Report no. 435, Milwaukee, Wisc., July, 1996.", keywords = "", referred = "" } @ARTICLE{Zerah1986a, author = "G.~Zerah and J.~P.~Hansen", month = "", year = 1986, title = "Self-Consistent Integral Equations for Fluid Pair Distribution Functions: {A}nother Attempt", journal = "J.~Chem.~Phys", volume = 84, number = "", pages = 2336, note = "", key = "Zerah1986a", abstract = "", comment = "", keywords = "", referred = "[Charpentier2001a]." } @ARTICLE{Zhang1994a, author = "Hong Zhang and Herschel A. Rabitz", month = "", year = 1994, title = "Robust Control of Quantum Molecular Systems in Presence of Disturbances and Uncertainties", journal = "Physical Review A", volume = 49, number = 4, pages = "2241--2254", note = "", key = "Zhang1994a", abstract = "", comment = "", keywords = "", referred = "[Ben-Haj-Yedder2001a]." } @TECHREPORT{Zhu1994a, author = "C.~Zhu and R.~H.~Byrd and P.~Lu and Jorge Nocedal", month = "", year = 1994, title = "{LBFGS-B}: {F}ortran Subroutines for Large-Scale Bound Constrained Optimization", number = "NAM-11", note = "", address = "Ill.", institution = "EECS Northwestern Univ.", key = "Zhu1994a", type = "Report", abstract = "", comment = "", keywords = "", referred = "[Kim2001a]." }