On Minimizing Some Merit Functions for Nonlinear Complementarity Problems under H-Differentiability

M. A. Tawhid () and J. L. Goffin ()
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M. A. Tawhid: Thompson Rivers University
J. L. Goffin: McGill University

Journal of Optimization Theory and Applications, 2008, vol. 139, issue 1, No 8, 127-140

Abstract: 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.

Keywords: H-differentiability; Semismooth-functions; Locally Lipschitzian functions; Nonlinear complementarity problems; NCP functions; Merit function; Descent algorithms (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10957-008-9409-z

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