A proximal point algorithm for the monotone second-order cone complementarity problem

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Abstract

This paper is devoted to the study of the proximal point algorithm for solving monotone second-order cone 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. Numerical comparisons are also made with the derivative-free descent method used by Pan and Chen (Optimization 59:1173-1197, 2010), which confirm the theoretical results and the effectiveness of the algorithm.

Original languageEnglish
Pages (from-to)1037-1063
Number of pages27
JournalComputational Optimization and Applications
Volume51
Issue number3
DOIs
Publication statusPublished - 2012 Apr 1

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Keywords

  • Approximation criterion
  • Complementarity problem
  • Proximal point algorithm
  • Second-order cone

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

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