Entering into the Domain of Feasible Solutions Using Interior Point Method

Abstract

The interior point algorithm for a linear programming problem is considered. The algorithm consists of two stages. At the first stage, we enter into the domain of feasible solutions for given constraints. The second stage lies in optimization over the feasible domain. Entering into the feasible domain is represented as an extended linear programming problem by adding only one new variable. The main goal of this paper is to provide a theoretical justification for the process of entering into the feasible domain under the assumption that the extended problem is nondegenerate.