A smoothing Newton method based on the generalized Fischer-Burmeister function for MCPs

Jein-Shan Chen, Shaohua Pan, Tzu Ching Lin

Research output: Contribution to journalArticle

12 Citations (Scopus)


We present a smooth approximation for the generalized Fischer-Burmeister function where the 2-norm in the FB function is relaxed to a general p-norm (p > 1), and establish some favorable properties for it - for example, the Jacobian consistency. With the smoothing function, we transform the mixed complementarity problem (MCP) into solving a sequence of smooth system of equations, and then trace a smooth path generated by the smoothing algorithm proposed by Chen (2000) [28] to the solution set. In particular, we investigate the influence of p on the numerical performance of the algorithm by solving all MCPLIP test problems, and conclude that the smoothing algorithm with p ∈ (1, 2] has better numerical performance than the one with p > 2.

Original languageEnglish
Pages (from-to)3739-3758
Number of pages20
JournalNonlinear Analysis, Theory, Methods and Applications
Issue number9-10
Publication statusPublished - 2010 May 1



  • Convergence rate
  • Mixed complementarity problem
  • Smoothing approximation
  • The generalized FB function

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this