Descent three-term conjugate gradient methods based on secant conditions for unconstrained optimization

Hiroshi Kobayashi, Yasushi Narushima, Hiroshi Yabe

Research output: Contribution to journalArticle


The conjugate gradient method is an effective method for large-scale unconstrained optimization problems. Recent research has proposed conjugate gradient methods based on secant conditions to establish fast convergence of the methods. However, these methods do not always generate a descent search direction. In contrast, Y. Narushima, H. Yabe, and J.A. Ford [A three-term conjugate gradient method with sufficient descent property for unconstrained optimization, SIAM J. Optim. 21 (2011), pp. 212–230] proposed a three-term conjugate gradient method which always satisfies the sufficient descent condition. This paper makes use of both ideas to propose descent three-term conjugate gradient methods based on particular secant conditions, and then shows their global convergence properties. Finally, numerical results are given.

Original languageEnglish
Pages (from-to)1313-1329
Number of pages17
JournalOptimization Methods and Software
Issue number6
Publication statusPublished - 2017 Nov 2
Externally publishedYes



  • global convergence
  • secant condition
  • sufficient descent property
  • three-term conjugate gradient method
  • unconstrained optimization

ASJC Scopus subject areas

  • Software
  • Control and Optimization
  • Applied Mathematics

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