EQUIPPING THE BARZILAI-BORWEIN METHOD WITH THE TWO DIMENSIONAL QUADRATIC TERMINATION PROPERTY

doi:10.1137/21M1390785

CSpace

	EQUIPPING THE BARZILAI-BORWEIN METHOD WITH THE TWO DIMENSIONAL QUADRATIC TERMINATION PROPERTY
	Ya-Kui Huang 1; Yu-Hong Dai 2,3; Xin-Wei Liu 1
	2021
发表期刊	SIAM JOURNAL ON OPTIMIZATION
ISSN	1052-6234
卷号	31 期号:4 页码:3068-3096
摘要	A novel gradient stepsize is derived at the motivation of equipping the BarzilaiBorwein (BB) method with the two dimensional quadratic termination property. A remarkable feature of the novel stepsize is that its computation only depends on the BB stepsizes in previous iterations and does not require any exact line search or the Hessian, and hence it can easily be extended for nonlinear optimization. By adaptively taking long BB steps and some short steps associated with the new stepsize, we develop an efficient gradient method for quadratic optimization and general unconstrained optimization and extend it to solve extreme eigenvalue problems. The proposed method is further extended for box-constrained optimization and singly linearly box-constrained optimization by incorporating gradient projection techniques. Numerical experiments demonstrate that the proposed method outperforms the most successful gradient methods in the literature.
关键词	Barzilai-Borwein method quadratic termination property unconstrained opti-mization extreme eigenvalue problem box-constrained optimization singly linearly box-constrained optimization
DOI	10.1137/21M1390785
收录类别	SCI
语种	英语
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 the Chinese Academy of Sciences[XDA27000000] ; Natural Science Foundation of Hebei Province[A2021202010] ; Beijing Academy of Artificial Intelligence (BAAI)
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000738355700023
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59839
专题	中国科学院数学与系统科学研究院
通讯作者	Yu-Hong Dai
作者单位	1.Hebei Univ Technol, Inst Math, Tianjin 300401, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Ya-Kui Huang,Yu-Hong Dai,Xin-Wei Liu. EQUIPPING THE BARZILAI-BORWEIN METHOD WITH THE TWO DIMENSIONAL QUADRATIC TERMINATION PROPERTY[J]. SIAM JOURNAL ON OPTIMIZATION,2021,31(4):3068-3096.
APA	Ya-Kui Huang,Yu-Hong Dai,&Xin-Wei Liu.(2021).EQUIPPING THE BARZILAI-BORWEIN METHOD WITH THE TWO DIMENSIONAL QUADRATIC TERMINATION PROPERTY.SIAM JOURNAL ON OPTIMIZATION,31(4),3068-3096.
MLA	Ya-Kui Huang,et al."EQUIPPING THE BARZILAI-BORWEIN METHOD WITH THE TWO DIMENSIONAL QUADRATIC TERMINATION PROPERTY".SIAM JOURNAL ON OPTIMIZATION 31.4(2021):3068-3096.