A semismooth newton method for SOCCPs based on a one-parametric class of SOC complementarity functions

Shaohua Pan, Jein Shan Chen

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41 Citations (Scopus)


In this paper, we present a detailed investigation for the properties of a one-parametric class of SOC complementarity functions, which include the globally Lipschitz continuity, strong semismoothness, and the characterization of their B-subdifferential. Moreover, for the merit functions induced by them for the second-order cone complementarity problem (SOCCP), we provide a condition for each stationary point to be a solution of the SOCCP and establish the boundedness of their level sets, by exploiting Cartesian P-properties. We also propose a semismooth Newton type method based on the reformulation of the nonsmooth system of equations involving the class of SOC complementarity functions. The global and superlinear convergence results are obtained, and among others, the superlinear convergence is established under strict complementarity. Preliminary numerical results are reported for DIMACS second-order cone programs, which confirm the favorable theoretical properties of the method.

Original languageEnglish
Pages (from-to)59-88
Number of pages30
JournalComputational Optimization and Applications
Issue number1
Publication statusPublished - 2010 Jan 1



  • B-subdifferential
  • Complementarity
  • Newton's method
  • Second-order cone
  • Semismooth

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

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