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Volume 10, Issue 3, Article 68 |
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An Unconstrained Optimization Technique for Nonsmooth Nonlinear Complementarity Problems
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Authors: |
M. Tawhid, |
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Keywords:
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Nonlinear complementarity problem, unconstrained minimization, NCP function, merit function, regularity conditions, nonsmooth function, descent algorithm. |
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Date Received:
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13/07/2009 |
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Date Accepted:
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22/07/2009 |
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Subject Codes: |
90C33, 90C20, 90C56, 49J52
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Editors: |
Ram U. Verma, |
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Abstract: |
In this article, we consider an unconstrained minimization formulation of the nonlinear complementarity problem NCP when the underlying functions are  -differentiable but not necessarily locally Lipschitzian or directionally differentiable. We show how, under appropriate regularity conditions on an -differential of  , minimizing the merit function corresponding to leads to a solution of the nonlinear complementarity problem. Our results give a unified treatment of such results for  -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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