AN APPROXIMATE PROXIMAL POINT ALGORITHM FOR NONLINEAR COMPLEMENTARITY PROBLEMS

Abstract

In this paper, we suggest and analyze a new method for solving nonlinear complementarity problems (NCP) where the underlying function F is co-coercive. The theme of this paper is twofold. First, we consider the logarithmic-quadratic proximal (LQP) method which was introduced by Auslender, Teboulle and Ben-Tiba (A logarithmic-quadratic proximal method for variational inequalities, Comput. Optim. Appl. 12, 31–40, 1999). Next, we propose a new modified LQP method by using a new direction with a new step size αk. We show that the method isglobally convergent. Some preliminary computational results are given to illustrate the efficiency of the proposed method.