A family of NCP functions and a descent method for the nonlinear complementarity problem

Jein-Shan Chen, Shaohua Pan

Research output: Contribution to journalArticle

62 Citations (Scopus)

Abstract

In last decades, there has been much effort on the solution and the analysis of the nonlinear complementarity problem (NCP) by reformulating NCP as an unconstrained minimization involving an NCP function. In this paper, we propose a family of new NCP functions, which include the Fischer-Burmeister function as a special case, based on a p-norm with p being any fixed real number in the interval (1,+∞), and show several favorable properties of the proposed functions. In addition, we also propose a descent algorithm that is indeed derivative-free for solving the unconstrained minimization based on the merit functions from the proposed NCP functions. Numerical results for the test problems from MCPLIB indicate that the descent algorithm has better performance when the parameter p decreases in (1,+∞). This implies that the merit functions associated with p (1,2), for example p=1.5, are more effective in numerical computations than the Fischer-Burmeister merit function, which exactly corresponds to p=2.

Original languageEnglish
Pages (from-to)389-404
Number of pages16
JournalComputational Optimization and Applications
Volume40
Issue number3
DOIs
Publication statusPublished - 2008 Jul 1

Fingerprint

Descent Method
Nonlinear Complementarity Problem
Merit Function
Unconstrained Minimization
Descent Algorithm
Derivative-free
Numerical Computation
Test Problems
Family
Nonlinear complementarity problem
Norm
Imply
Numerical Results
Decrease
Interval
Derivatives

Keywords

  • Descent method
  • Merit function
  • NCP
  • NCP function

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

Cite this

A family of NCP functions and a descent method for the nonlinear complementarity problem. / Chen, Jein-Shan; Pan, Shaohua.

In: Computational Optimization and Applications, Vol. 40, No. 3, 01.07.2008, p. 389-404.

Research output: Contribution to journalArticle

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