KMS Of Academy of mathematics and systems sciences, CAS
| A SEMISMOOTH NEWTON METHOD FOR SEMIDEFINITE PROGRAMS AND ITS APPLICATIONS IN ELECTRONIC STRUCTURE CALCULATIONS | |
Li, Yongfeng1,2; Wen, Zaiwen1,2; Yang, Chao3; Yuan, Ya-Xiang4
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| 2018 | |
| Source Publication | SIAM JOURNAL ON SCIENTIFIC COMPUTING
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| ISSN | 1064-8275 |
| Volume | 40Issue:6Pages:A4131-A4157 |
| Abstract | The well-known interior point method for semidefinite progams can only be used to tackle problems of relatively small scales. First-order methods such as the the alternating direction method of multipliers (ADMM) have much lower computational cost per iteration. However, their convergence can be slow, especially for obtaining highly accurate approximations. In this paper, we present a practical and efficient second-order semismooth Newton type method based on solving a fixed-point mapping derived from an equivalent form of the ADMM. We discuss a number of techniques that can be used to improve the computational efficiency of the method and achieve global convergence. Then we further consider the application in electronic structure calculations. The ground state energy of a many-electron system can be approximated by an variational approach in which the total energy of the system is minimized with respect to one- and two-body reduced density matrices instead of many-electron wavefunctions. This problem can be formulated as a semidefinite programming problem. Extensive numerical experiments show that our approach is competitive to the state-of-the-art methods in terms of both accuracy and speed. |
| Keyword | semidefinite programming ADMM semismooth Newton method electronic structure calculation two-body reduced density matrix |
| DOI | 10.1137/18M1188069 |
| Language | 英语 |
| Funding Project | NSFC[11331012] ; NSFC[11461161005] ; NSFC[11831002] ; NSFC[11421101] ; NSFC[91330202] ; National Basic Research Project[2015CB856002] ; Scientific Discovery through Advanced Computing (SciDAC) program - U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research (Basic Energy Sciences) ; Center for Applied Mathematics for Energy Research Applications (CAMERA)[DE-SC0008666] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000453747800019 |
| Publisher | SIAM PUBLICATIONS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/31843 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Li, Yongfeng |
| Affiliation | 1.Peking Univ, Beijing Int Ctr Math Res, Beijing, Peoples R China 2.Peking Univ, Ctr Data Sci, Beijing, Peoples R China 3.Lawrence Berkeley Natl Lab, Computat Res Div, Berkeley, CA 94720 USA 4.Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp, Beijing, Peoples R China |
| Recommended Citation GB/T 7714 | Li, Yongfeng,Wen, Zaiwen,Yang, Chao,et al. A SEMISMOOTH NEWTON METHOD FOR SEMIDEFINITE PROGRAMS AND ITS APPLICATIONS IN ELECTRONIC STRUCTURE CALCULATIONS[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2018,40(6):A4131-A4157. |
| APA | Li, Yongfeng,Wen, Zaiwen,Yang, Chao,&Yuan, Ya-Xiang.(2018).A SEMISMOOTH NEWTON METHOD FOR SEMIDEFINITE PROGRAMS AND ITS APPLICATIONS IN ELECTRONIC STRUCTURE CALCULATIONS.SIAM JOURNAL ON SCIENTIFIC COMPUTING,40(6),A4131-A4157. |
| MLA | Li, Yongfeng,et al."A SEMISMOOTH NEWTON METHOD FOR SEMIDEFINITE PROGRAMS AND ITS APPLICATIONS IN ELECTRONIC STRUCTURE CALCULATIONS".SIAM JOURNAL ON SCIENTIFIC COMPUTING 40.6(2018):A4131-A4157. |
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