On the acceleration of the Barzilai–Borwein method

Yakui Huang (), Yu-Hong Dai (), Xin-Wei Liu () and Hongchao Zhang ()
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Yakui Huang: Hebei University of Technology
Yu-Hong Dai: Chinese Academy of Sciences
Xin-Wei Liu: Hebei University of Technology
Hongchao Zhang: Louisiana State University

Computational Optimization and Applications, 2022, vol. 81, issue 3, No 2, 717-740

Abstract: Abstract The Barzilai–Borwein (BB) gradient method is efficient for solving large-scale unconstrained problems to modest accuracy due to its ingenious stepsize which generally yields nonmonotone behavior. In this paper, we propose a new stepsize to accelerate the BB method by requiring finite termination for minimizing the two-dimensional strongly convex quadratic function. Based on this new stepsize, we develop an efficient gradient method for quadratic optimization which adaptively takes the nonmonotone BB stepsizes and certain monotone stepsizes. Two variants using retard stepsizes associated with the new stepsize are also presented. Numerical experiments show that our strategies of properly inserting monotone gradient steps into the nonmonotone BB method could significantly improve its performance and our new methods are competitive with the most successful gradient descent methods developed in the recent literature.

Keywords: Barzilai–Borwein method; Gradient methods; Finite termination; Quadratic optimization; 90C20; 90C25; 90C30 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10589-022-00349-z

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