AN APPROXIMATE PROXIMAL POINT ALGORITHM FOR NONLINEAR COMPLEMENTARITY PROBLEMS

Year 2012, Volume: 41 Issue: 1, 103 - 117, 01.01.2012

A. Bnouhachem M.a. Noor Muhammad Aslam Noor M. Khalfaoui S. Zhaohan

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 is
globally convergent. Some preliminary computational results are given to illustrate the efficiency of the proposed method.

Keywords

Nonlinear complementarity problems , Co-coercive operator , Logarithmicquadratic proximal method , 2000 AMS Classification: 49 J 40

AN APPROXIMATE PROXIMAL POINT ALGORITHM FOR NONLINEAR COMPLEMENTARITY PROBLEMS

Abstract

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