STRUCTURED QUASI-NEWTON METHODS FOR OPTIMIZATION WITH ORTHOGONALITY CONSTRAINTS

doi:10.1137/18M121112X

	STRUCTURED QUASI-NEWTON METHODS FOR OPTIMIZATION WITH ORTHOGONALITY CONSTRAINTS
	Hu, Jiang 1; Jiang, Bo 2; Lin, Lin 3; Wen, Zaiwen 1; Yuan, Ya-Xiang4
	2019
发表期刊	SIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN	1064-8275
卷号	41 期号:4 页码:A2239-A2269
摘要	In this paper, we study structured quasi-Newton methods for optimization problems with orthogonality constraints. Note that the Riemannian Hessian of the objective function requires both the Euclidean Hessian and the Euclidean gradient. In particular, we are interested in applications that the Euclidean Hessian itself consists of a computational cheap part and a significantly expensive part. Our basic idea is to keep these parts of lower computational costs but substitute those parts of higher computational costs by the limited-memory quasi-Newton update. More specifically, the part related to the Euclidean gradient and the cheaper parts in the Euclidean Hessian are preserved. The initial quasi-Newton matrix is further constructed from a limited-memory Nystrom approximation to the expensive part. Consequently, our subproblems approximate the original objective function in the Euclidean space and preserve the orthogonality constraints without performing the so-called vector transports. When the subproblems are solved to sufficient accuracy, both global and local q-superlinear convergence can be established under mild conditions. Preliminary numerical experiments on the linear eigenvalue problem and the electronic structure calculation show the effectiveness of our method compared with the state-of-art algorithms.
关键词	optimization with orthogonality constraints structured quasi-Newton method limited-memory Nystrom approximation Hartree-Fock total energy minimization
DOI	10.1137/18M121112X
语种	英语
资助项目	NSFC[11501298] ; NSFC[11671036] ; NSFC[11831002] ; NSFC[11421101] ; NSFC[91730302] ; NSFC[11331012] ; NSFC[11461161005] ; Young Elite Scientists Sponsorship Program by CAST[2017QNRC001] ; NSF of Jiangsu Province[BK20150965] ; National Science Foundation[DMS-1652330] ; Department of Energy[DE-SC0017867] ; Department of Energy[DE-AC02-05CH11231] ; SciDAC project ; National Basic Research Project[2015CB856002]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000483924100008
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/35653
专题	计算数学与科学工程计算研究所
通讯作者	Hu, Jiang
作者单位	1.Peking Univ, Beijing Int Ctr Math Res, Beijing, Peoples R China 2.Nanjing Normal Univ, Sch Math Sci, Key Lab NSLSCS Jiangsu Prov, Nanjing 210023, Jiangsu, Peoples R China 3.Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA 4.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Hu, Jiang,Jiang, Bo,Lin, Lin,et al. STRUCTURED QUASI-NEWTON METHODS FOR OPTIMIZATION WITH ORTHOGONALITY CONSTRAINTS[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2019,41(4):A2239-A2269.
APA	Hu, Jiang,Jiang, Bo,Lin, Lin,Wen, Zaiwen,&Yuan, Ya-Xiang.(2019).STRUCTURED QUASI-NEWTON METHODS FOR OPTIMIZATION WITH ORTHOGONALITY CONSTRAINTS.SIAM JOURNAL ON SCIENTIFIC COMPUTING,41(4),A2239-A2269.
MLA	Hu, Jiang,et al."STRUCTURED QUASI-NEWTON METHODS FOR OPTIMIZATION WITH ORTHOGONALITY CONSTRAINTS".SIAM JOURNAL ON SCIENTIFIC COMPUTING 41.4(2019):A2239-A2269.