An Unconstrained Optimization Technique for Nonsmooth Nonlinear Complementarity Problems

In this article, we consider an unconstrained minimization formulation of the nonlinear complementarity problem NCP(f) when the underlying functions are H-differentiable but not necessarily locally Lipschitzian or directionally differentiable. We show how, under appropriate regularity conditions on an H-differential of f , minimizing the merit function corresponding to f leads to a solution of the nonlinear complementarity problem. Our results give a unified treatment of such results for C-functions, semismooth-functions, and for locally Lipschitzian functions. We also show a result on the global convergence of a derivative-free descent algorithm for solving nonsmooth nonlinear complementarity problem.