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An application of \(H\)-differentiability to nonnegative and unrestricted generalized complementarity problems. (English) Zbl 1147.90405
Summary: 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, \({\mathbf P}_{0}\)-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.

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
49J50 Fréchet and Gateaux differentiability in optimization
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