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A NEW FIRST-ORDER ALGORITHMIC FRAMEWORK FOR OPTIMIZATION PROBLEMS WITH ORTHOGONALITY CONSTRAINTS
Gao, Bin1,2; Liu, Xin1,2; Chen, Xiaojun3; Yuan, Ya-Xiang1
2018
Source PublicationSIAM JOURNAL ON OPTIMIZATION
ISSN1052-6234
Volume28Issue:1Pages:302-332
AbstractIn this paper, we consider a class of optimization problems with orthogonality constraints, the feasible region of which is called the Stiefel manifold. Our new framework combines a function value reduction step with a correction step. Different from the existing approaches, the function value reduction step of our algorithmic framework searches along the standard Euclidean descent directions instead of the vectors in the tangent space of the Stiefel manifold, and the correction step further reduces the function value and guarantees a symmetric dual variable at the same time. We construct two types of algorithms based on this new framework. The first type is based on gradient reduction including the gradient reflection (GR) and the gradient projection (GP) algorithms. The other one adopts a columnwise block coordinate descent (CBCD) scheme with a novel idea for solving the corresponding CBCD subproblem inexactly. We prove that both GR/GP with a fixed step size and CBCD belong to our algorithmic framework, and any clustering point of the iterates generated by the proposed framework is a first-order stationary point. Preliminary experiments illustrate that our new framework is of great potential.
Keywordorthogonality constraint Stiefel manifold Householder transformation gradient projection block coordinate descent
DOI10.1137/16M1098759
Language英语
Funding ProjectNSFC[11622112] ; NSFC[11471325] ; NSFC[91530204] ; NSFC[11688101] ; NSFC[11331012] ; NSFC[11461161005] ; National Center for Mathematics and Interdisciplinary Sciences, CAS ; Key Research Program of Frontier Sciences, CAS ; Hong Kong Research Council[N_PolyU504/14]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000424527900012
PublisherSIAM PUBLICATIONS
Citation statistics
Cited Times:2[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29680
Collection计算数学与科学工程计算研究所
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp, Beijing, Peoples R China
2.Univ Chinese Acad Sci, Beijing, Peoples R China
3.Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Hong Kong, Peoples R China
Recommended Citation
GB/T 7714
Gao, Bin,Liu, Xin,Chen, Xiaojun,et al. A NEW FIRST-ORDER ALGORITHMIC FRAMEWORK FOR OPTIMIZATION PROBLEMS WITH ORTHOGONALITY CONSTRAINTS[J]. SIAM JOURNAL ON OPTIMIZATION,2018,28(1):302-332.
APA Gao, Bin,Liu, Xin,Chen, Xiaojun,&Yuan, Ya-Xiang.(2018).A NEW FIRST-ORDER ALGORITHMIC FRAMEWORK FOR OPTIMIZATION PROBLEMS WITH ORTHOGONALITY CONSTRAINTS.SIAM JOURNAL ON OPTIMIZATION,28(1),302-332.
MLA Gao, Bin,et al."A NEW FIRST-ORDER ALGORITHMIC FRAMEWORK FOR OPTIMIZATION PROBLEMS WITH ORTHOGONALITY CONSTRAINTS".SIAM JOURNAL ON OPTIMIZATION 28.1(2018):302-332.
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