New efficient descent direction of a primal-dual path-following algorithm for linear programming

Abstract

We introduce a new primal-dual interior-point algorithm with a full-Newton step for solving linear optimization problems. The newly proposed approach is based on applying a new function on a simple equivalent form of the centering equation of the system, which defines the central path. Thus, we get a new efficient search direction for the considered algorithm. Moreover, we prove that the method solves the studied problems in polynomial time and that the algorithm obtained has the best known complexity bound for linear optimization. Finally, a comparative numerical study is reported to show the efficiency of the proposed algorithm.