Properties of a family of generalized NCP-functions and a derivative free algorithm for complementarity problems

Sheng Long Hu, Zheng Hai Huang, Jein-Shan Chen

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31 Citations (Scopus)

Abstract

In this paper, we propose a new family of NCP-functions and the corresponding merit functions, which are the generalization of some popular NCP-functions and the related merit functions. We show that the new NCP-functions and the corresponding merit functions possess a system of favorite properties. Specially, we show that the new NCP-functions are strongly semismooth, Lipschitz continuous, and continuously differentiable; and that the corresponding merit functions have S C1 property (i.e., they are continuously differentiable and their gradients are semismooth) and L C1 property (i.e., they are continuously differentiable and their gradients are Lipschitz continuous) under suitable assumptions. Based on the new NCP-functions and the corresponding merit functions, we investigate a derivative free algorithm for the nonlinear complementarity problem and discuss its global convergence. Some preliminary numerical results are reported.

Original languageEnglish
Pages (from-to)69-82
Number of pages14
JournalJournal of Computational and Applied Mathematics
Volume230
Issue number1
DOIs
Publication statusPublished - 2009 Aug 1

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Keywords

  • Complementarity problem
  • Derivative free algorithm
  • Merit function
  • NCP-function

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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