A family of spectral gradient methods for optimization

被引：1
作者：
Yu-Hong Dai
Yakui Huang
Xin-Wei Liu
机构：
[1] Chinese Academy of Sciences,LSEC, ICMSEC, Academy of Mathematics and Systems Science
[2] University of Chinese Academy of Sciences,Mathematical Sciences
[3] Hebei University of Technology,Institute of Mathematics
来源：
Computational Optimization and Applications | 2019年 / 74卷
关键词：
Unconstrained optimization; Steepest descent method; Spectral gradient method; -linear convergence; -superlinear convergence;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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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页码：43 / 65
页数：22
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