On the log-exponential trajectory of linear programming

Abstract

Development in interior point methods has suggested various solution trajectories, also called central paths, for linear programming. In this paper we define a new central path through a log-exponential perturbation to the complementarity equation in the Karush-Kuhn-Tucker system. The behavior of this central path is investigated and an algorithm is proposed. The algorithm can compute an ε-optimal solution at a superlinear rate of convergence. © 2003 Kluwer Academic Publishers.