A framework of constraint preserving update schemes for optimization on Stiefel manifold

doi:10.1007/s10107-014-0816-7

	A framework of constraint preserving update schemes for optimization on Stiefel manifold
	Jiang, Bo; Dai, Yu-Hong
	2015-11-01
发表期刊	MATHEMATICAL PROGRAMMING
ISSN	0025-5610
卷号	153 期号:2 页码:535-575
摘要	This paper considers optimization problems on the Stiefel manifold (XX)-X-T = I-p, where X is an element of R-nxp is the variable and I-p is the p-by-p identity matrix. A framework of constraint preserving update schemes is proposed by decomposing each feasible point into the range space of X and the null space of X-T. While this general framework can unify many existing schemes, a new update scheme with low complexity cost is also discovered. Then we study a feasible Barzilai-Borwein-like method under the new update scheme. The global convergence of the method is established with an adaptive nonmonotone line search. The numerical tests on the nearest low-rank correlation matrix problem, the Kohn-Sham total energy minimization and a specific problem from statistics demonstrate the efficiency of the new method. In particular, the new method performs remarkably well for the nearest low-rank correlation matrix problem in terms of speed and solution quality and is considerably competitive with the widely used SCF iteration for the Kohn-Sham total energy minimization.
关键词	Stiefel manifold Orthogonality constraint Sphere constraint Range space Null space Barzilai-Borwein-like method Feasible Adaptive nonmonotone line search Low-rank correlation matrix Kohn-Sham total energy minimization Heterogeneous quadratic functions
DOI	10.1007/s10107-014-0816-7
语种	英语
资助项目	National Key Basic Research Program of China[2015CB856000] ; China National Funds for Distinguished Young Scientists[11125107] ; Chinese NSF[10831106] ; Chinese NSF[81211130105] ; CAS grant[kjcx-yw-s7-03]
WOS研究方向	Computer Science ; Operations Research & Management Science ; Mathematics
WOS类目	Computer Science, Software Engineering ; Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000364330300010
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/21157
专题	计算数学与科学工程计算研究所
通讯作者	Dai, Yu-Hong
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Jiang, Bo,Dai, Yu-Hong. A framework of constraint preserving update schemes for optimization on Stiefel manifold[J]. MATHEMATICAL PROGRAMMING,2015,153(2):535-575.
APA	Jiang, Bo,&Dai, Yu-Hong.(2015).A framework of constraint preserving update schemes for optimization on Stiefel manifold.MATHEMATICAL PROGRAMMING,153(2),535-575.
MLA	Jiang, Bo,et al."A framework of constraint preserving update schemes for optimization on Stiefel manifold".MATHEMATICAL PROGRAMMING 153.2(2015):535-575.