Two classes of merit functions for the second-order cone complementarity problem

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37 Citations (Scopus)

Abstract

Recently Tseng (Math Program 83:159-185, 1998) extended a class of merit functions, proposed by Luo and Tseng (A new class of merit functions for the nonlinear complementarity problem, in Complementarity and Variational Problems: State of the Art, pp. 204-225, 1997), for the nonlinear complementarity problem (NCP) to the semidefinite complementarity problem (SDCP) and showed several related properties. In this paper, we extend this class of merit functions to the second-order cone complementarity problem (SOCCP) and show analogous properties as in NCP and SDCP cases. In addition, we study another class of merit functions which are based on a slight modification of the aforementioned class of merit functions. Both classes of merit functions provide an error bound for the SOCCP and have bounded level sets.

Original languageEnglish
Pages (from-to)495-519
Number of pages25
JournalMathematical Methods of Operations Research
Volume64
Issue number3
DOIs
Publication statusPublished - 2006 Dec 1

Keywords

  • Error bound
  • Jordan product
  • Level set
  • Merit function
  • Second-order cone
  • Spectral factorization

ASJC Scopus subject areas

  • Software
  • Mathematics(all)
  • Management Science and Operations Research

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