The Jacobian consistency of a smoothed Fischer-Burmeister function associated with second-order cones

Hideho Ogasawara, Yasushi Narushima

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

This paper deals with the second-order cone complementarity problem (SOCCP), which is an important class of problems containing various optimization problems. The SOCCP can be reformulated as a system of nonsmooth equations. For solving this system of nonsmooth equations, smoothing Newton methods are widely used. The Jacobian consistency property plays an important role for achieving a rapid convergence of the methods. In this paper, we show the Jacobian consistency of a smoothed Fischer-Burmeister function. Moreover, we estimate the distance between the subgradient of the Fischer-Burmeister function and the gradient of its smoothing function.

Original languageEnglish
Pages (from-to)231-247
Number of pages17
JournalJournal of Mathematical Analysis and Applications
Volume394
Issue number1
DOIs
Publication statusPublished - 2012 Oct 1
Externally publishedYes

Fingerprint

Nonsmooth Equations
Second-order Cone
Complementarity Problem
Cones
Smoothing Newton Method
Smoothing Function
Subgradient
Newton-Raphson method
Gradient
Optimization Problem
Estimate
Class

Keywords

  • Jacobian consistency
  • Second-order cone complementarity problem
  • Smoothed Fischer-Burmeister function

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

The Jacobian consistency of a smoothed Fischer-Burmeister function associated with second-order cones. / Ogasawara, Hideho; Narushima, Yasushi.

In: Journal of Mathematical Analysis and Applications, Vol. 394, No. 1, 01.10.2012, p. 231-247.

Research output: Contribution to journalArticle

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