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STRUCTURED QUASI-NEWTON METHODS FOR OPTIMIZATION WITH ORTHOGONALITY CONSTRAINTS

文献类型：期刊论文

作者Hu, Jiang4; Jiang, Bo3; Lin, Lin2; Wen, Zaiwen4; Yuan, Ya-Xiang1
刊名SIAM JOURNAL ON SCIENTIFIC COMPUTING
出版日期2019
卷号41期号:4页码:A2239-A2269
关键词optimization with orthogonality constraints structured quasi-Newton method limited-memory Nystrom approximation Hartree-Fock total energy minimization
ISSN号1064-8275
DOI10.1137/18M121112X
英文摘要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.
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
语种英语
WOS记录号WOS:000483924100008
出版者SIAM PUBLICATIONS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/35652]  
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.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Beijing, Peoples R China
2.Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA
3.Nanjing Normal Univ, Sch Math Sci, Key Lab NSLSCS Jiangsu Prov, Nanjing 210023, Jiangsu, Peoples R China
4.Peking Univ, Beijing Int Ctr Math Res, 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.

入库方式： OAI收割

来源：数学与系统科学研究院

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