Interior-point methods for optimization

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,...

Interior Point Methods for Nonlinear Optimization