Interior Point Algorithms and Applications

Abstract

Modern interior point methods originated from an algorithm introduced by Karmarkar in 1984 for linear programming. In the years since then, and software for linear programming have become quite popular, while extensions to more general classes of problems, such as convex quadratic programming, linear complementarity problem, semi-definite programming, second order cone programming and nonconvex and nonlinear problems, have reached varying levels of maturity. In this paper we review the interior point and applications in some optimization problems, such as linear programming, linear complementarity problem, semi-definite programming and some convex programming. Combining with the current studies, we conclude that applications of interior point and kernel function-based interior point algorithms will be the research focuses in the future.