On Minimizing Some Merit Functions for Nonlinear Complementarity Problems under H-Differentiability |
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Authors: | M. A. Tawhid J. L. Goffin |
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Affiliation: | (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;(2) Faculty of Management, McGill University, 1001 Sherbrooke Street West, Montreal, PQ, H3A 1G5, Canada |
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Abstract: | In this paper, we describe the H-differentials of some well known NCP functions and their merit functions. We show how, under appropriate conditions on an H-differential of f, minimizing a merit function corresponding to f leads to a solution of the nonlinear complementarity problem. Our results give a unified treatment of such results for C 1-functions, semismooth-functions, and locally Lipschitzian functions. Illustrations are given to show the usefulness of our results. We present also a result on the global convergence of a derivative-free descent algorithm for solving the nonlinear complementarity problem. The first author is deeply indebted to Professor M. Seetharama Gowda for his numerous helpful suggestions and encouragement. Special thanks to Professor J.-P. Crouzeix and an anonymous referees for their constructive suggestions which led to numerous improvements in the paper. The research of the first author was supported in part by the Natural Sciences and Engineering Research Council of Canada and Scholar Activity Grant of Thompson Rivers University. The research of the second author was supported by the Natural Sciences and Engineering Research Council of Canada. |
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Keywords: | H-differentiability Semismooth-functions Locally Lipschitzian functions Nonlinear complementarity problems NCP functions Merit function Descent algorithms |
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