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

Jein Shan Chen, Hung Ta Gao, Shaohua Pan

研究成果: 雜誌貢獻文章同行評審

20 引文 斯高帕斯(Scopus)

摘要

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: ψp (a, b) = frac(1, 2) [{norm of matrix} (a, b) {norm of matrix}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 ψp 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.

原文英語
頁(從 - 到)455-471
頁數17
期刊Journal of Computational and Applied Mathematics
232
發行號2
DOIs
出版狀態已發佈 - 2009 十月 15

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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