中国科学院机构知识库网格
Chinese Academy of Sciences Institutional Repositories Grid
A NEW FIRST-ORDER ALGORITHMIC FRAMEWORK FOR OPTIMIZATION PROBLEMS WITH ORTHOGONALITY CONSTRAINTS

文献类型:期刊论文

作者Gao, Bin1,2; Liu, Xin1,2; Chen, Xiaojun3; Yuan, Ya-Xiang1
刊名SIAM JOURNAL ON OPTIMIZATION
出版日期2018
卷号28期号:1页码:302-332
关键词orthogonality constraint Stiefel manifold Householder transformation gradient projection block coordinate descent
ISSN号1052-6234
DOI10.1137/16M1098759
英文摘要In 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.
资助项目NSFC[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研究方向Mathematics
语种英语
WOS记录号WOS:000424527900012
出版者SIAM PUBLICATIONS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/29679]  
专题计算数学与科学工程计算研究所
通讯作者Gao, Bin
作者单位1.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
推荐引用方式
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.

入库方式: OAI收割

来源:数学与系统科学研究院

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