Extended Barzilai-Borwein method for unconstrained minimization problems

Yasushi Narushima(narusimars.kagu.tus.ac.jp)
Takahiko Wakamatsu(brfft303ybb.ne.jp)
Hiroshi Yabe(yabers.kagu.tus.ac.jp)

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 requires few storage locations and inexpensive computations. Therefore, several 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 method and establish global and Q-superlinear convergence properties of the proposed method for minimizing a strictly convex quadratic function. Furthermore, we discuss an application of our method to general objective functions. Finally, some numerical experiments are given.

Keywords: Unconstrained optimization, the Barzilai-Borwein method, global and Q-superlinear convergence

Category 1: Nonlinear Optimization (Unconstrained Optimization )

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Entry Submitted: 05/21/2008
Entry Accepted: 05/21/2008
Entry Last Modified: 05/21/2008

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