Randomized interior point methods for sampling and optimization

Randomized Interior Point methods for Sampling and Optimization

We present a Markov Chain, “Dikin walk”, for sampling from a convex body equipped with a self-concordant barrier. This Markov Chain corresponds to a natural random walk with respect to a Riemannian metric defined using the Hessian of the barrier function. For every convex set of dimension n, there exists a self-concordant barrier whose self-concordance parameter is O(n). Consequently, a rapidly...

Interior-point methods for optimization

This article describes the current state of the art of interior-point methods (IPMs) for convex, conic, and general nonlinear optimization. We discuss the theory, outline the algorithms, and comment on the applicability of this class of methods, which have revolutionized the field over the last twenty years.

Interior Point Methods for Combinatorial Optimization

Research on using interior point algorithms to solve combinatorial optimization and integer programming problems is surveyed. This paper discusses branch and cut methods for integer programming problems, a potential reduction method based on transforming an integer programming problem to an equivalent nonconvex quadratic programming problem, interior point methods for solving network flow probl...

Interior Point Methods for Linear Optimization: Exercises

Interior Point Methods for Nondiierentiable Optimization

We describe the analytic center cutting plane method and its relationship to classical methods of nondi erentiable optimization and column generation. Implementation issues are also discussed, and current applications listed. Keywords Projective Algorithm, Analytic Center, Cutting Plane Method. This work has been completed with support from the Fonds National Suisse de la Recherche Scienti que,...