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

Research output: Contribution to journalArticle

30 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

Fingerprint

NCP Function
Derivative-free
Merit Function
Complementarity Problem
Generalized Functions
Derivatives
Continuously differentiable
Lipschitz
Gradient
Nonlinear Complementarity Problem
Global Convergence
Family
Numerical Results

Keywords

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

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

Properties of a family of generalized NCP-functions and a derivative free algorithm for complementarity problems. / Hu, Sheng Long; Huang, Zheng Hai; Chen, Jein-Shan.

In: Journal of Computational and Applied Mathematics, Vol. 230, No. 1, 01.08.2009, p. 69-82.

Research output: Contribution to journalArticle

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