A family of spectral gradient methods for optimization

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

Computational Optimization and Applications, 2019, vol. 74, issue 1, No 2, 43-65

Abstract: Abstract We propose a family of spectral gradient methods, whose stepsize is determined by a convex combination of the long Barzilai–Borwein (BB) stepsize and the short BB stepsize. Each member of the family is shown to share certain quasi-Newton property in the sense of least squares. The family also includes some other gradient methods as its special cases. We prove that the family of methods is R-superlinearly convergent for two-dimensional strictly convex quadratics. Moreover, the family is R-linearly convergent in the any-dimensional case. Numerical results of the family with different settings are presented, which demonstrate that the proposed family is promising.

Keywords: Unconstrained optimization; Steepest descent method; Spectral gradient method; R-linear convergence; R-superlinear convergence (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10589-019-00107-8

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