Extension of interior point method for linear programming

Abstract

We have highlighted in our study of linear programming problem that are of great importance in problems that mimic real life. The aim of our study is to present a theoretical, algorithmic and numerical study of the logarithmic Barrier method for resolving Linear Programming problem (LP). Firstly, we determine the direction by Newton’s method. Then, we establish an efficient algorithm to compute the displacement step according to the direction with the technic of approximate functions. We present the conceptual results that ensure the existence and uniqueness of the optimal solution to the approximate problem of LP as well as its convergence to the optimal solution of the initial problem. Finally, their convergence results well confirmed. The results obtained through the numerical study allowed us to give some conclusions regarding the behavior of the proposed approximate function to find the displacement step then, the optimal solution to the problem.