Extended Barzilai-Borwein method for unconstrained minimization problems

Yasushi Narushima, Takahiko Wakamatsu, Hiroshi Yabe

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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
Issue number3
Publication statusPublished - 2010 Nov 9
Externally publishedYes


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

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics


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