An R-linearly convergent derivative-free algorithm for nonlinear complementarity problems based on the generalized Fischer-Burmeister merit function

  • Authors:

  • Jein-Shan Chen;Hung-Ta Gao;Shaohua Pan

  • Affiliations:

  • Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan;Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan;School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, China

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2009

Quantified Score

Hi-index 7.29

Visualization

Abstract

In the paper [J.-S. Chen, S. Pan, A family of NCP-functions and a descent method for the nonlinear complementarity problem, Computational Optimization and Applications, 40 (2008) 389-404], the authors proposed a derivative-free descent algorithm for nonlinear complementarity problems (NCPs) by the generalized Fischer-Burmeister merit function: @j"p(a,b)=12[@?(a,b)@?"p-(a+b)]^2, and observed that the choice of the parameter p has a great influence on the numerical performance of the algorithm. In this paper, we analyze the phenomenon theoretically for a derivative-free descent algorithm which is based on a penalized form of @j"p and uses a different direction from that of Chen and Pan. More specifically, we show that the algorithm proposed is globally convergent and has a locally R-linear convergence rate, and furthermore, its convergence rate will become worse when the parameter p decreases. Numerical results are also reported for the test problems from MCPLIB, which further verify the theoretical results obtained.