Abstract
This paper deals with nonnegative nonsmooth generalized complementarity problem, denoted by GCP(f,g). Starting with H-differentiable functions f and g, we describe H-differentials of some GCP functions and their merit functions. We show how, under appropriate conditions on H-differentials of f and g, minimizing a merit function corresponding to f and g leads to a solution of the generalized complementarity problem. Moreover, we generalize the concepts of monotonicity, P 0-property and their variants for functions and use them to establish some conditions to get a solution for generalized complementarity problem. Our results are generalizations of such results for nonlinear complementarity problem when the underlying functions are C 1, semismooth, and locally Lipschitzian.
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