The penalized Fischer-Burmeister SOC complementarity function

Shaohua Pan, Jein Shan Chen, Sangho Kum, Yongdo Lim

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this paper, we study the properties of the penalized Fischer-Burmeister (FB) second-order cone (SOC) complementarity function. We show that the function possesses similar desirable properties of the FB SOC complementarity function for local convergence; for example, with the function the second-order cone complementarity problem (SOCCP) can be reformulated as a (strongly) semismooth system of equations, and the corresponding nonsmooth Newton method has local quadratic convergence without strict complementarity of solutions. In addition, the penalized FB merit function has bounded level sets under a rather weak condition which can be satisfied by strictly feasible monotone SOCCPs or SOCCPs with the Cartesian R 01-property, although it is not continuously differentiable. Numerical results are included to illustrate the theoretical considerations.

Original languageEnglish
Pages (from-to)457-491
Number of pages35
JournalComputational Optimization and Applications
Volume49
Issue number3
DOIs
Publication statusPublished - 2011 Jul 1

Fingerprint

Second-order Cone
Complementarity
Cones
Local Quadratic Convergence
Strict Complementarity
Merit Function
Complementarity Problem
Local Convergence
Continuously differentiable
Bounded Set
Cartesian
Level Set
Newton Methods
System of equations
Newton-Raphson method
Monotone
Strictly
Numerical Results

Keywords

  • B-subdifferential
  • Coerciveness
  • Nonsmooth Newton method
  • Penalized Fischer-Burmeister function
  • Second-order cone complementarity problem

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

Cite this

The penalized Fischer-Burmeister SOC complementarity function. / Pan, Shaohua; Chen, Jein Shan; Kum, Sangho; Lim, Yongdo.

In: Computational Optimization and Applications, Vol. 49, No. 3, 01.07.2011, p. 457-491.

Research output: Contribution to journalArticle

Pan, Shaohua ; Chen, Jein Shan ; Kum, Sangho ; Lim, Yongdo. / The penalized Fischer-Burmeister SOC complementarity function. In: Computational Optimization and Applications. 2011 ; Vol. 49, No. 3. pp. 457-491.
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