Interior Point Algorithms in Linear Optimization

Abstract

This is a survey of the results concerning the development and study of the interior point algorithms. Some families of the direct and dual algorithms are considered. These algorithms entering the domain of feasible solutions take into account the objective function, which makes it possible to obtain the first feasible solution close to the optimal solution. The main results on the theoretical justification of algorithms are given. Recommendations are proposed concerning the advantages of individual variants of algorithms on the basis of the obtained theoretical results, available experimental studies, and experience of using algorithms in the models of energy engineering. Some numerically efficient version of the polynomial optimization algorithm in the cone of the central path is also presented.