A damped Gauss-Newton method for the second-order cone complementarity problem

Shaohua Pan, Jein-Shan Chen

Research output: Contribution to journalArticle

37 Citations (Scopus)

Abstract

We investigate some properties related to the generalized Newton method for the Fischer-Burmeister (FB) function over second-order cones, which allows us to reformulate the second-order cone complementarity problem (SOCCP) as a semismooth system of equations. Specifically, we characterize the B-subdifferential of the FB function at a general point and study the condition for every element of the B-subdifferential at a solution being nonsingular. In addition, for the induced FB merit function, we establish its coerciveness and provide a weaker condition than Chen and Tseng (Math. Program. 104:293-327, 2005) for each stationary point to be a solution, under suitable Cartesian P-properties of the involved mapping. By this, a damped Gauss-Newton method is proposed, and the global and superlinear convergence results are obtained. Numerical results are reported for the second-order cone programs from the DIMACS library, which verify the good theoretical properties of the method.

Original languageEnglish
Pages (from-to)293-318
Number of pages26
JournalApplied Mathematics and Optimization
Volume59
Issue number3
DOIs
Publication statusPublished - 2009 Jun 1

Fingerprint

Gauss-Newton Method
Second-order Cone
Complementarity Problem
Newton-Raphson method
Damped
Cones
Subdifferential
Generalized Newton Method
Coerciveness
Merit Function
Superlinear Convergence
Stationary point
Cartesian
Global Convergence
Convergence Results
System of equations
Verify
Numerical Results

Keywords

  • B-subdifferential
  • Complementarity
  • Fischer-Burmeister function
  • Generalized Newton method
  • Second-order cones

ASJC Scopus subject areas

  • Applied Mathematics
  • Control and Optimization

Cite this

A damped Gauss-Newton method for the second-order cone complementarity problem. / Pan, Shaohua; Chen, Jein-Shan.

In: Applied Mathematics and Optimization, Vol. 59, No. 3, 01.06.2009, p. 293-318.

Research output: Contribution to journalArticle

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