Globally Convergent Three-Term Conjugate Gradient Methods that Use Secant Conditions and Generate Descent Search Directions for Unconstrained Optimization

Kaori Sugiki, Yasushi Narushima, Hiroshi Yabe

Research output: Contribution to journalArticle

41 Citations (Scopus)

Abstract

In this paper, we propose a three-term conjugate gradient method based on secant conditions for unconstrained optimization problems. Specifically, we apply the idea of Dai and Liao (in Appl. Math. Optim. 43: 87-101, 2001) to the three-term conjugate gradient method proposed by Narushima et al. (in SIAM J. Optim. 21: 212-230, 2011). Moreover, we derive a special-purpose three-term conjugate gradient method for a problem, whose objective function has a special structure, and apply it to nonlinear least squares problems. We prove the global convergence properties of the proposed methods. Finally, some numerical results are given to show the performance of our methods.

Original languageEnglish
Pages (from-to)733-757
Number of pages25
JournalJournal of Optimization Theory and Applications
Volume153
Issue number3
DOIs
Publication statusPublished - 2012 Jun 1
Externally publishedYes

Fingerprint

Conjugate gradient method
Unconstrained Optimization
Conjugate Gradient Method
Chord or secant line
Descent
Term
Nonlinear Least Squares Problem
Global Convergence
Convergence Properties
Objective function
Optimization Problem
Numerical Results
Gradient

Keywords

  • Descent search direction
  • Global convergence
  • Secant condition
  • Three-term conjugate gradient method
  • Unconstrained optimization

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

Cite this

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AB - In this paper, we propose a three-term conjugate gradient method based on secant conditions for unconstrained optimization problems. Specifically, we apply the idea of Dai and Liao (in Appl. Math. Optim. 43: 87-101, 2001) to the three-term conjugate gradient method proposed by Narushima et al. (in SIAM J. Optim. 21: 212-230, 2011). Moreover, we derive a special-purpose three-term conjugate gradient method for a problem, whose objective function has a special structure, and apply it to nonlinear least squares problems. We prove the global convergence properties of the proposed methods. Finally, some numerical results are given to show the performance of our methods.

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