A Smoothing Newton Method with Fischer-Burmeister Function for Second-Order Cone Complementarity Problems

Yasushi Narushima, Nobuko Sagara, Hideho Ogasawara

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

The second-order cone complementarity problem (SOCCP) is an important class of problems containing a lot of optimization problems. The SOCCP can be transformed into a system of nonsmooth equations. To solve this nonsmooth system, smoothing techniques are often used. Fukushima, Luo and Tseng (SIAM J. Optim. 12:436-460, 2001) studied concrete theories and properties of smoothing functions for the SOCCP. Recently, a practical computational method using the smoothed natural residual function to solve the SOCCP was given by Chen, Sun and Sun (Comput. Optim. Appl. 25:39-56, 2003). In the present paper, we propose an algorithm to solve the SOCCP by using the smoothed Fischer-Burmeister function. Some preliminary numerical results are given.

Original languageEnglish
Pages (from-to)79-101
Number of pages23
JournalJournal of Optimization Theory and Applications
Volume149
Issue number1
DOIs
Publication statusPublished - 2011 Feb 1
Externally publishedYes

Fingerprint

Smoothing Newton Method
Second-order Cone
Complementarity Problem
Newton-Raphson method
Cones
Sun
Nonsmooth Equations
Smoothing Function
Smoothing Techniques
Computational methods
Computational Methods
Smoothing
Complementarity
Concretes
Optimization Problem
Numerical Results

Keywords

  • Fischer-Burmeister function
  • Global convergence
  • Second-order cone complementarity problem
  • Smoothing method
  • Superlinear convergence

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

Cite this

A Smoothing Newton Method with Fischer-Burmeister Function for Second-Order Cone Complementarity Problems. / Narushima, Yasushi; Sagara, Nobuko; Ogasawara, Hideho.

In: Journal of Optimization Theory and Applications, Vol. 149, No. 1, 01.02.2011, p. 79-101.

Research output: Contribution to journalArticle

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