A UNIFIED INTERIOR POINT FRAMEWORK FOR OPTIMIZATION ALGORITHMS

Abstract

Interior Point algorithms are optimization methods developed over the last three decades following the 1984 fundamental paper of Karmarkar. Over this period, IPM algorithms have had a profound impact on optimization theory as well as practice and have been successfully applied to many problems of business, engineering and science. Because of their operational simplicity and wide applicability, IPM algorithms are now playing an increasingly important role in computational optimization and operations research. This article provides unified interior point algorithms to optimization problems as well as comparing performances with classical algorithms.

Keywords Interior Point methods, Optimization algorithms, Lagrangian Multipliers,  Barrier methods, Newton’s method, Matrix-free method.