Interior Point Methods, Florian A. Potra, University of Maryland, Wed, 21 January, 2009, 10:00 a.m. C-356
The modern era of interior-point methods dates to 1984, when Karmarkar proposed his algorithm for linear programming. In the years since then, algorithms and software for linear programming have become quite sophisticated, while extensions to more general classes of problems, such as convex quadratic programming, semidefinite programming, and nonconvex problems, have reached varying levels of maturity. The first part of the talk will review the most important results in interior-point methods ob- tained over the past twenty five years, emphasizing the distinction between computational complexity and superlinear convergence. While the work on computational complexity has shown that interior-point methods can solve in polynomial time some important mathematical programming problems, superlinear convergence results explain why the practical performance of interior-point methods is better than predicted by the computational com- plexity results. The second part of the talk will concentrate on some recent results obtained by the speaker and his collaborators.