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arXiv · 1812.02974

A family of spectral gradient methods for optimization

Yu-Hong Dai·Yakui Huang·Xin-Wei Liu
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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.

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Yu-Hong Dai, Yakui Huang, Xin-Wei Liu. 2018-12-07. A family of spectral gradient methods for optimization. https://arxiv.org/abs/1812.02974

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