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  Volume 10, Issue 3, Article 68
An Unconstrained Optimization Technique for Nonsmooth Nonlinear Complementarity Problems

    Authors: M. Tawhid,  
    Keywords: Nonlinear complementarity problem, unconstrained minimization, NCP function, merit function, regularity conditions, nonsmooth function, descent algorithm.  
    Date Received: 13/07/2009  
    Date Accepted: 22/07/2009  
    Subject Codes:

90C33, 90C20, 90C56, 49J52

    Editors: Ram U. Verma,  

In this article, we consider an unconstrained minimization formulation of the nonlinear complementarity problem NCP$ (f)$ when the underlying functions are $ H$-differentiable but not necessarily locally Lipschitzian or directionally differentiable. We show how, under appropriate regularity conditions on an $ H$-differential of $ f$, minimizing the 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 for locally Lipschitzian functions. We also show a result on the global convergence of a derivative-free descent algorithm for solving nonsmooth nonlinear complementarity problem.

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