STABILIZED BARZILAI-BORWEIN METHOD

doi:10.4208/jcm.1911-m2019-0171

	STABILIZED BARZILAI-BORWEIN METHOD
	Burdakov, Oleg 1; Dai, Yuhong 3; Huang, Na 2
刊名	JOURNAL OF COMPUTATIONAL MATHEMATICS
	2019
卷号	37 期号:6 页码:916-936
关键词	Unconstrained optimization Spectral algorithms Stabilization Convergence analysis
ISSN号	0254-9409
DOI	10.4208/jcm.1911-m2019-0171
英文摘要	The Barzilai-Borwein (BB) method is a popular and efficient tool for solving large-scale unconstrained optimization problems. Its search direction is the same as for the steepest descent (Cauchy) method, but its stepsize rule is different. Owing to this, it converges much faster than the Cauchy method. A feature of the BB method is that it may generate too long steps, which throw the iterates too far away from the solution. Moreover, it may not converge, even when the objective function is strongly convex. In this paper, a stabilization technique is introduced. It consists in bounding the distance between each pair of successive iterates, which often allows for decreasing the number of BB iterations. When the BB method does not converge, our simple modification of this method makes it convergent. For strongly convex functions with Lipschits gradients, we prove its global convergence, despite the fact that no line search is involved, and only gradient values are used. Since the number of stabilization steps is proved to be finite, the stabilized version inherits the fast local convergence of the BB method. The presented results of extensive numerical experiments show that our stabilization technique often allows the BB method to solve problems in a fewer iterations, or even to solve problems where the latter fails.
资助项目	Visiting Scientist award under the Chinese Academy of Sciences President's International Fellowship Initiative ; Chinese Natural Science Foundation[11631013] ; National 973 Program of China[2015CB856002]
WOS研究方向	Mathematics
语种	英语
出版者	GLOBAL SCIENCE PRESS
WOS记录号	WOS:000504738100009
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/50492]
专题	中国科学院数学与系统科学研究院
通讯作者	Huang, Na
作者单位	1.Linkoping Univ, Dept Math, Linkoping, Sweden 2.China Agr Univ, Coll Sci, Dept Appl Math, Beijing 100083, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Burdakov, Oleg,Dai, Yuhong,Huang, Na. STABILIZED BARZILAI-BORWEIN METHOD[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2019,37(6):916-936.
APA	Burdakov, Oleg,Dai, Yuhong,&Huang, Na.(2019).STABILIZED BARZILAI-BORWEIN METHOD.JOURNAL OF COMPUTATIONAL MATHEMATICS,37(6),916-936.
MLA	Burdakov, Oleg,et al."STABILIZED BARZILAI-BORWEIN METHOD".JOURNAL OF COMPUTATIONAL MATHEMATICS 37.6(2019):916-936.