Title: Solving non-linear complementarity problem by a derivative-free descent method

Authors: Mohamed A. Tawhid

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

Abstract: The non-linear complementarity problem (NCP) has many important applications in operations research, economic equilibrium, models, mathematical programming, engineering and mechanics. In this paper, we consider smooth NCP on the basis of the square Kanzow–Kleinmichel function. We show under certain assumptions, any stationary point of the unconstrained minimisation problem is already a solution of smooth NCP. Also, we suggest a derivative-free descent algorithm and give conditions for its convergence. Furthermore, we present some preliminary numerical results.

Keywords: smooth NCP; nonlinear complementarity problem; unconstrained minimisation; NCP functions; merit functions; descent algorithms.

DOI: 10.1504/IJOR.2011.038906

International Journal of Operational Research, 2011 Vol.10 No.3, pp.361 - 375

Published online: 14 Feb 2015 *

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