A Fliter Method for Sloving LCP Based on Nonmonotone Line Search

Abstract

In this paper, we propose a filter method to solve the linear complementarity problem(LCP). By using the Fisher-Burmeister function, we convert the LCP to an equivalent optimization problem with linear equality constraints. A filter approach is employed to tackle the optimization problem and the proposed mechanism for accepting the trial step is obtained by a nonmonotone filter technique. Under some conditions, we establish the global convergence of the algorithm.