The talk deals with research on efficient methods for solving nonlinear programming problems, i.e., smooth finite-dimensional optimization problems. Such problems arise in many different disciplines, e.g., engineering and finance.
For the problems considered, Newton's method may be viewed as the model method for achieving fast asymptotic convergence. Loosely speaking, interior methods extend Newton's method by creating barriers at the boundary of the feasible region.
Primal-dual interior methods have proved very powerful for solving linear and convex optimization problems. In the talk, nonconvex problems are considered. Different types of interior methods will be discussed, emphasizing the features of the primal-dual methods. Extensions to semidefinite programming and numerical aspects of large-scale problems will also be given.
The talk is based on joint research with Philip E. Gill (UCSD).