Multi-step nonlinear conjugate gradient methods for unconstrained minimization

John A. Ford, Yasushi Narushima, Hiroshi Yabe

研究成果: Article査読

36 被引用数 (Scopus)

抄録

Conjugate gradient methods are appealing for large scale nonlinear optimization problems, because they avoid the storage of matrices. Recently, seeking fast convergence of these methods, Dai and Liao (Appl. Math. Optim. 43:87-101, 2001) proposed a conjugate gradient method based on the secant condition of quasi-Newton methods, and later Yabe and Takano (Comput. Optim. Appl. 28:203-225, 2004) proposed another conjugate gradient method based on the modified secant condition. In this paper, we make use of a multi-step secant condition given by Ford and Moghrabi (Optim. Methods Softw. 2:357-370, 1993; J. Comput. Appl. Math. 50:305-323, 1994) and propose two new conjugate gradient methods based on this condition. The methods are shown to be globally convergent under certain assumptions. Numerical results are reported.

本文言語English
ページ(範囲)191-216
ページ数26
ジャーナルComputational Optimization and Applications
40
2
DOI
出版ステータスPublished - 2008 6 1
外部発表はい

ASJC Scopus subject areas

  • 制御と最適化
  • 計算数学
  • 応用数学

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