Interior Point Methods (IPMs)
Department of Informatics
University of Bergen, Norway

We introduce a new primal-dual IPMs based on new class of kernel functions which differs from the class of self-regular kernel functions. The class is defined by some simple conditions on the kernel function. These properties enable us to derive many new and tight estimates that greatly simplify the analysis of IPMs based on these kernel functions and reduce the gap from small-update and Large-update. A generalizations of the methods that ere developed for linear optimization to the very important cases of semidefinite optimization and linear complementarity problems.

We also consider the effect of solving the primal-dual system using an iterative method. We give an efficient preconditioner and show how the accuracy of the approximate solution of the linear systems influences the convergence of the IPM.

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Last modified: February 5, 2010 by M. El Ghami