On minimizing the implicit Lagrangian for nonlinear complementarity problems under H-differentiability

In this paper, we describe H-differential of the implicit Lagrangian function. We show how, under appropriate regularity conditions on an H-differential of f, minimizing the implicit Lagrangian 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 and for locally Lipschitzian functions.