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An application of H-differentiability to nonnegative and unrestricted generalized complementarity problems

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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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  1. Department of Mathematics and Statistics, School of Advanced Technologies and Mathematics, Thompson Rivers University, 900 McGill Road, PO Box 3010, Kamloops, BC, V2C 5N3, Canada

    M. A. Tawhid

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Tawhid, M.A. An application of H-differentiability to nonnegative and unrestricted generalized complementarity problems. Comput Optim Appl 39, 51–74 (2008). https://doi.org/10.1007/s10589-007-9052-x

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