A smoothing conjugate gradient method for solving systems of nonsmooth equations

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Many problems in real world are reduced to systems of nonsmooth equations and hence many researchers study numerical methods for solving systems of nonsmooth equations. As numerical methods for solving systems of nonsmooth equations, Newton-like methods are known as efficient numerical methods. However, these methods are not necessarily applied directly to large-scale problems, because these methods need to store matrices. In this paper, we propose a smoothing method which is based on the nonlinear conjugate gradient method and does not store any matrices for solving systems of nonsmooth equations. In addition, we prove the global convergence property of the proposed method under standard assumptions. Finally, we give some preliminary numerical results.

Original languageEnglish
Pages (from-to)8646-8655
Number of pages10
JournalApplied Mathematics and Computation
Volume219
Issue number16
DOIs
Publication statusPublished - 2013 Apr 17
Externally publishedYes

Fingerprint

Nonsmooth Equations
Conjugate gradient method
Conjugate Gradient Method
Smoothing
Numerical methods
Numerical Methods
Newton-like Method
Smoothing Methods
Large-scale Problems
Global Convergence
Convergence Properties
Numerical Results

Keywords

  • Conjugate gradient method
  • Global convergence
  • Smoothing method
  • Systems of nonsmooth equations

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics

Cite this

A smoothing conjugate gradient method for solving systems of nonsmooth equations. / Narushima, Yasushi.

In: Applied Mathematics and Computation, Vol. 219, No. 16, 17.04.2013, p. 8646-8655.

Research output: Contribution to journalArticle

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