Error bounds for symmetric cone complementarity problems

Xin He Miao, Jein Shan Chen

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In this paper, we investigate the issue of error bounds for symmetric cone complementarity problems (SCCPs). In particular, we show that the distance between an arbitrary point in Euclidean Jordan algebra and the solution set of the symmetric cone complementarity problem can be bounded above by some merit functions such as Fischer-Burmeister merit function, the natural residual function and the implicit Lagrangian function. The so-called R0-type conditions, which are new and weaker than existing ones in the literature, are assumed to guarantee that such merit functions can provide local and global error bounds for SCCPs. Moreover, when SCCPs reduce to linear cases, we demonstrate such merit functions cannot serve as global error bounds under general monotone condition, which implicitly indicates that the proposed R0-type conditions cannot be replaced by P-type conditions which include monotone condition as special cases.

Original languageEnglish
Pages (from-to)627-641
Number of pages15
JournalNumerical Algebra, Control and Optimization
Volume3
Issue number4
DOIs
Publication statusPublished - 2013 Oct 1

Keywords

  • Error bounds
  • Merit function
  • R-type functions
  • Symmetric cone complementarity problem

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Control and Optimization
  • Applied Mathematics

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