Multi-step nonlinear conjugate gradient methods for unconstrained minimization

John A. Ford, Yasushi Narushima, Hiroshi Yabe

Research output: Contribution to journalArticlepeer-review

44 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)191-216
Number of pages26
JournalComputational Optimization and Applications
Issue number2
Publication statusPublished - 2008 Jun 1
Externally publishedYes


  • Conjugate gradient method
  • Global convergence
  • Line search
  • Multi-step secant condition
  • Unconstrained optimization

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics


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