Paper Title:

Equivalence of the Nonsmooth Nonlinear Complementarity Problems to Unconstrained Minimization

Author(s):

M. A. Tawhid and J. L. Goffin

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
Alexandria University and Egypt Japan University of Science and Technology,
Alexandria-Egypt
mtawhid@tru.ca  

Faculty of Management, McGill University,
1001 Sherbrooke Street West, Montreal, Quebec, H3A 1G5
Canada.
Jean-Louis.Goffin@McGill.ca 
 

Abstract:

This paper deals with nonsmooth nonlinear complementarity problem, where the underlying functions are nonsmooth which admit the H-differentiability but not necessarily locally Lipschitzian or directionally differentiable. We consider a reformulation of the nonlinear complementarity problem as an unconstrained minimization problem. We describe H-differentials of the associated penalized Fischer-Burmeister and Kanzow and Kleinmichel merit functions. We show how, under appropriate P₀, semimonotone (E₀), P, positive definite, and strictly semimonotone (E) -conditions on an H-differential of f, finding local/global minimum of a merit function (or a `stationary point' of a merit function) leads to a solution of the given nonlinear complementarity problem. Our results not only give new results but also unify/extend various similar results proved for C¹.

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