Proximal point algorithm for nonlinear complementarity problem based on the generalized fischer-burmeister merit function

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Abstract

This paper is devoted to the study of the proximal point algorithm for solving monotone and nonmonotone nonlinear complementarity problems. The proximal point algorithm is to generate a sequence by solving subproblems that are regularizations of the original problem. After given an appropriate criterion for approximate solutions of subproblems by adopting a merit function, the proximal point algorithm is verified to have global and superlinear convergence properties. For the purpose of solving the subproblems efficiently, we introduce a generalized Newton method and show that only one Newton step is eventually needed to obtain a desired approximate solution that approximately satisfies the appropriate criterion under mild conditions. The motivations of this paper are twofold. One is analyzing the proximal point al-gorithm based on the generalized Fischer-Burmeister function which includes the Fischer-Burmeister function as special case, another one is trying to see if there are relativistic change on numerical performance when we adjust the parameter in the generalized Fischer-Burmeister.

Original languageEnglish
Pages (from-to)153-169
Number of pages17
JournalJournal of Industrial and Management Optimization
Volume9
Issue number1
DOIs
Publication statusPublished - 2013 Mar 26

Keywords

  • Approximation criterion
  • Complementarity problem
  • Proximal point algorithm

ASJC Scopus subject areas

  • Business and International Management
  • Strategy and Management
  • Control and Optimization
  • Applied Mathematics

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