On the acceleration of the Barzilai-Borwein method

doi:10.1007/s10589-022-00349-z

	On the acceleration of the Barzilai-Borwein method
	Huang, Yakui 3; Dai, Yu-Hong 2; Liu, Xin-Wei 3; Zhang, Hongchao 1
刊名	COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
	2022-01-13
页码	24
关键词	Barzilai-Borwein method Gradient methods Finite termination Quadratic optimization
ISSN号	0926-6003
DOI	10.1007/s10589-022-00349-z
英文摘要	The Barzilai-Borwein (BB) gradient method is efficient for solving large-scale unconstrained problems to modest accuracy due to its ingenious stepsize which generally yields nonmonotone behavior. In this paper, we propose a new stepsize to accelerate the BB method by requiring finite termination for minimizing the two-dimensional strongly convex quadratic function. Based on this new stepsize, we develop an efficient gradient method for quadratic optimization which adaptively takes the nonmonotone BB stepsizes and certain monotone stepsizes. Two variants using retard stepsizes associated with the new stepsize are also presented. Numerical experiments show that our strategies of properly inserting monotone gradient steps into the nonmonotone BB method could significantly improve its performance and our new methods are competitive with the most successful gradient descent methods developed in the recent literature.
资助项目	National Natural Science Foundation of China[11701137] ; National Natural Science Foundation of China[11631013] ; National Natural Science Foundation of China[12071108] ; National Natural Science Foundation of China[11671116] ; National Natural Science Foundation of China[11991021] ; National Natural Science Foundation of China[12021001] ; Strategic Priority Research Program of Chinese Academy of Sciences[XDA27000000] ; China Scholarship Council[201806705007] ; Natural Science Foundation of Hebei Province[A2021202010] ; USA National Science Foundation[2110722] ; USA National Science Foundation[1819161] ; Beijing Academy of Artificial Intelligence (BAAI)
WOS研究方向	Operations Research & Management Science ; Mathematics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000742263000002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/59865]
专题	中国科学院数学与系统科学研究院
通讯作者	Huang, Yakui
作者单位	1.Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 3.Hebei Univ Technol, Inst Math, Tianjin 300401, Peoples R China
推荐引用方式 GB/T 7714	Huang, Yakui,Dai, Yu-Hong,Liu, Xin-Wei,et al. On the acceleration of the Barzilai-Borwein method[J]. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,2022:24.
APA	Huang, Yakui,Dai, Yu-Hong,Liu, Xin-Wei,&Zhang, Hongchao.(2022).On the acceleration of the Barzilai-Borwein method.COMPUTATIONAL OPTIMIZATION AND APPLICATIONS,24.
MLA	Huang, Yakui,et al."On the acceleration of the Barzilai-Borwein method".COMPUTATIONAL OPTIMIZATION AND APPLICATIONS (2022):24.