Extended Barzilai-Borwein method for unconstrained minimization problems

Yasushi Narushima, Takahiko Wakamatsu, Hiroshi Yabe

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

In 1988, Barzilai and Borwein presented a new choice of step size for the gradient method for solving unconstrained minimization problems. Their method aimed to accelerate the convergence of the steepest descent method. The Barzilai-Borwein method has a low storage requirement and inexpensive computations. Therefore, many authors have paid attention to the Barzilai-Borwein method and have proposed some variants to solve large-scale unconstrained minimization problems. In this paper, we extend the Barzilai-Borwein-type methods of Friedlander et al. to more general class and establish global and Q-superlinear convergence properties of the proposed method for minimizing a strictly convex quadratic function. Furthermore, we apply our method to general objective functions. Finally, some numerical experiments are given.

Original languageEnglish
Pages (from-to)591-613
Number of pages23
JournalPacific Journal of Optimization
Volume6
Issue number3
Publication statusPublished - 2010 Nov 9
Externally publishedYes

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Unconstrained Minimization
Minimization Problem
Steepest descent method
Gradient methods
Steepest Descent Method
Superlinear Convergence
Experiments
Gradient Method
Strictly Convex
Quadratic Function
Convergence Properties
Convex function
Accelerate
Objective function
Numerical Experiment
Requirements

Keywords

  • Barzilai-Borwein method
  • Global convergence
  • Large-scale unconstrained minimization problem
  • Q-superlinear convergence

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

Cite this

Extended Barzilai-Borwein method for unconstrained minimization problems. / Narushima, Yasushi; Wakamatsu, Takahiko; Yabe, Hiroshi.

In: Pacific Journal of Optimization, Vol. 6, No. 3, 09.11.2010, p. 591-613.

Research output: Contribution to journalArticle

Narushima, Yasushi ; Wakamatsu, Takahiko ; Yabe, Hiroshi. / Extended Barzilai-Borwein method for unconstrained minimization problems. In: Pacific Journal of Optimization. 2010 ; Vol. 6, No. 3. pp. 591-613.
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