R-linear convergence of the Barzilai and Borwein gradient method

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	R-linear convergence of the Barzilai and Borwein gradient method
	Dai, YH ; Liao, LZ
	2002
发表期刊	IMA JOURNAL OF NUMERICAL ANALYSIS
ISSN	0272-4979
卷号	22 期号:1 页码:1-10
摘要	Combined with non-monotone line search, the Barzilai and Borwein (BB) gradient method has been successfully extended for solving unconstrained optimization problems and is competitive with conjugate gradient methods. In this paper, we establish the R-linear convergence of the BB method for any-dimensional strongly convex quadratics. One corollary of this result is that the BB method is also locally R-linear convergent for general objective functions, and hence the stepsize in the BB method will always be accepted by the non-monotone line search when the iterate is close to the solution.
关键词	unconstrained optimization gradient method R-linear convergence strictly convex
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000173395600001
出版者	OXFORD UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/17379
专题	中国科学院数学与系统科学研究院
通讯作者	Dai, YH
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci & Engn Comp, Beijing 100080, Peoples R China 2.Hong Kong Baptist Univ, Dept Math, Kowloon, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	Dai, YH,Liao, LZ. R-linear convergence of the Barzilai and Borwein gradient method[J]. IMA JOURNAL OF NUMERICAL ANALYSIS,2002,22(1):1-10.
APA	Dai, YH,&Liao, LZ.(2002).R-linear convergence of the Barzilai and Borwein gradient method.IMA JOURNAL OF NUMERICAL ANALYSIS,22(1),1-10.
MLA	Dai, YH,et al."R-linear convergence of the Barzilai and Borwein gradient method".IMA JOURNAL OF NUMERICAL ANALYSIS 22.1(2002):1-10.