A merit function method for infinite-dimensional SOCCPs

Yungyen Chiang, Shaohua Pan, Jein Shan Chen

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We introduce the Jordan product associated with the second-order cone K into the real Hilbert space H, and then define a one-parametric class of complementarity functions φt on H×H with the parameter t∈[0,2). We show that the squared norm of φt with tφ(0,2) is a continuously F(réchet)-differentiable merit function. By this, the second-order cone complementarity problem (SOCCP) in H can be converted into an unconstrained smooth minimization problem involving this class of merit functions, and furthermore, under the monotonicity assumption, every stationary point of this minimization problem is shown to be a solution of the SOCCP.

Original languageEnglish
Pages (from-to)159-178
Number of pages20
JournalJournal of Mathematical Analysis and Applications
Volume383
Issue number1
DOIs
Publication statusPublished - 2011 Nov 1

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Keywords

  • Complementarity
  • Hilbert space
  • Merit functions
  • Second-order cone

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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