Nonlinear conjugate gradient methods with structured secant condition for nonlinear least squares problems

Michiya Kobayashi, Yasushi Narushima, Hiroshi Yabe

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

In this paper, we deal with conjugate gradient methods for solving nonlinear least squares problems. Several Newton-like methods have been studied for solving nonlinear least squares problems, which include the Gauss-Newton method, the Levenberg-Marquardt method and the structured quasi-Newton methods. On the other hand, conjugate gradient methods are appealing for general large-scale nonlinear optimization problems. By combining the structured secant condition and the idea of Dai and Liao (2001) [20], the present paper proposes conjugate gradient methods that make use of the structure of the Hessian of the objective function of nonlinear least squares problems. The proposed methods are shown to be globally convergent under some assumptions. Finally, some numerical results are given.

Original languageEnglish
Pages (from-to)375-397
Number of pages23
JournalJournal of Computational and Applied Mathematics
Volume234
Issue number2
DOIs
Publication statusPublished - 2010 May 15
Externally publishedYes

Keywords

  • Conjugate gradient method
  • Global convergence
  • Least squares problems
  • Line search
  • Structured secant condition

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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