KMS Of Academy of mathematics and systems sciences, CAS
| STRUCTURED QUASI-NEWTON METHODS FOR OPTIMIZATION WITH ORTHOGONALITY CONSTRAINTS | |
Hu, Jiang1; Jiang, Bo2; Lin, Lin3; Wen, Zaiwen1; Yuan, Ya-Xiang4
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| 2019 | |
| Source Publication | SIAM JOURNAL ON SCIENTIFIC COMPUTING
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| ISSN | 1064-8275 |
| Volume | 41Issue:4Pages:A2239-A2269 |
| Abstract | 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. |
| Keyword | optimization with orthogonality constraints structured quasi-Newton method limited-memory Nystrom approximation Hartree-Fock total energy minimization |
| DOI | 10.1137/18M121112X |
| Language | 英语 |
| Funding Project | 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 Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000483924100008 |
| Publisher | SIAM PUBLICATIONS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/35653 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Hu, Jiang |
| Affiliation | 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 |
| Recommended Citation 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. |
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