90C33, 90C20, 90C56, 49J52

In this article, we consider an unconstrained minimization formulation of the nonlinear complementarity problem NCP when the underlying functions are -differentiable but not necessarily locally Lipschitzian or directionally differentiable. We show how, under appropriate regularity conditions on an -differential of , minimizing the merit function corresponding to leads to a solution of the nonlinear complementarity problem. Our results give a unified treatment of such results for -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. ;