A SEMISMOOTH NEWTON METHOD FOR SEMIDEFINITE PROGRAMS AND ITS APPLICATIONS IN ELECTRONIC STRUCTURE CALCULATIONS

doi:10.1137/18M1188069

	A SEMISMOOTH NEWTON METHOD FOR SEMIDEFINITE PROGRAMS AND ITS APPLICATIONS IN ELECTRONIC STRUCTURE CALCULATIONS
	Li, Yongfeng 1,2; Wen, Zaiwen 1,2; Yang, Chao 3; Yuan, Ya-Xiang4
	2018
发表期刊	SIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN	1064-8275
卷号	40 期号:6 页码:A4131-A4157
摘要	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.
关键词	semidefinite programming ADMM semismooth Newton method electronic structure calculation two-body reduced density matrix
DOI	10.1137/18M1188069
语种	英语
资助项目	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研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000453747800019
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/31843
专题	计算数学与科学工程计算研究所
通讯作者	Li, Yongfeng
作者单位	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
推荐引用方式 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.