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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
2018
Source PublicationSIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN1064-8275
Volume40Issue:6Pages:A4131-A4157
AbstractThe 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.
Keywordsemidefinite programming ADMM semismooth Newton method electronic structure calculation two-body reduced density matrix
DOI10.1137/18M1188069
Language英语
Funding ProjectNSFC[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 AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000453747800019
PublisherSIAM PUBLICATIONS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/31843
Collection计算数学与科学工程计算研究所
Affiliation1.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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