A family of spectral gradient methods for optimization

doi:10.1007/s10589-019-00107-8

	A family of spectral gradient methods for optimization
	Dai, Yu-Hong1,2 ; Huang, Yakui 3; Liu, Xin-Wei 3
	2019-09-01
发表期刊	COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
ISSN	0926-6003
卷号	74 期号:1 页码:43-65
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.
关键词	Unconstrained optimization Steepest descent method Spectral gradient method R-linear convergence R-superlinear convergence
DOI	10.1007/s10589-019-00107-8
语种	英语
资助项目	National Natural Science Foundation of China[11631013] ; National Natural Science Foundation of China[11701137] ; National Natural Science Foundation of China[11671116] ; National 973 Program of China[2015CB856002]
WOS研究方向	Operations Research & Management Science ; Mathematics
WOS类目	Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000476600200002
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/35309
专题	计算数学与科学工程计算研究所
通讯作者	Huang, Yakui
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Math Sci, Beijing 100049, Peoples R China 3.Hebei Univ Technol, Inst Math, Tianjin 300401, Peoples R China
推荐引用方式 GB/T 7714	Dai, Yu-Hong,Huang, Yakui,Liu, Xin-Wei. A family of spectral gradient methods for optimization[J]. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,2019,74(1):43-65.
APA	Dai, Yu-Hong,Huang, Yakui,&Liu, Xin-Wei.(2019).A family of spectral gradient methods for optimization.COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,74(1),43-65.
MLA	Dai, Yu-Hong,et al."A family of spectral gradient methods for optimization".COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 74.1(2019):43-65.