On Minimizing Some Merit Functions for Nonlinear Complementarity Problems under H-Differentiability

Abstract

In this paper, we describe the H-differentials of some well known NCP functions and their merit functions. We show how, under appropriate conditions on an H-differential of f, minimizing a merit function corresponding to f leads to a solution of the nonlinear complementarity problem. Our results give a unified treatment of such results for C1-functions, semismooth-functions, and locally Lipschitzian functions. Illustrations are given to show the usefulness of our results. We present also a result on the global convergence of a derivative-free descent algorithm for solving the nonlinear complementarity problem.