KMS Of Academy of mathematics and systems sciences, CAS
| EXACT PENALTY FUNCTION FOR \ell2,1 NORM MINIMIZATION OVER THE STIEFEL MANIFOLD | |
| Xiao, Nachuan1,2; Liu, Xin1,2; Ya-Xiang Yuan1 | |
| 2021 | |
| Source Publication | SIAM JOURNAL ON OPTIMIZATION
 |
| ISSN | 1052-6234 |
| Volume | 31Issue:4Pages:3097-3126 |
| Abstract | \ell 2,1 norm minimization with orthogonality constraints, which comprise a feasible region called the Stiefel manifold, has wide applications in statistics and data science. The state-ofthe-art approaches adopt a proximal gradient technique on either the Stiefel manifold or its tangent spaces. The consequent subproblem does not have a closed-form solution and hence requires an iterative procedure to solve, which is usually time-consuming. In this paper, we discover that the Lagrangian multipliers of the orthogonality constraints in this class of problems are of closed-form expressions. By using this closed-form expression, we introduce a penalty function for this type of problem. We theoretically demonstrate the equivalence between the penalty function and the original \ell 2,1 norm minimization under mild assumptions. Based on the exact penalty function, we propose an inexact proximal gradient method in which the subproblem is of closed-form solution. The global convergence and the worst case complexity are established. Numerical experiments illustrate the advantages of our method when compared with the existing proximal-based first-order methods. |
| Keyword | orthogonality constraint Stiefel manifold nonsmooth optimization augmented Lagrangian method |
| DOI | 10.1137/20M1354313 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China[11971466] ; National Natural Science Foundation of China[11991021] ; National Natural Science Foundation of China[11991020] ; Key Research Program of Frontier Sciences, Chinese Academy of Sciences[ZDBS-LY-7022] ; National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences ; Youth Innovation Promotion Association, Chinese Academy of Sciences ; NSFC[11688101] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000738355700024 |
| Publisher | SIAM PUBLICATIONS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/59836 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Xiao, Nachuan |
| Affiliation | 1.Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Beijing 100049, Peoples R China |
| Recommended Citation GB/T 7714 | Xiao, Nachuan,Liu, Xin,Ya-Xiang Yuan. EXACT PENALTY FUNCTION FOR \ell2,1 NORM MINIMIZATION OVER THE STIEFEL MANIFOLD[J]. SIAM JOURNAL ON OPTIMIZATION,2021,31(4):3097-3126. |
| APA | Xiao, Nachuan,Liu, Xin,&Ya-Xiang Yuan.(2021).EXACT PENALTY FUNCTION FOR \ell2,1 NORM MINIMIZATION OVER THE STIEFEL MANIFOLD.SIAM JOURNAL ON OPTIMIZATION,31(4),3097-3126. |
| MLA | Xiao, Nachuan,et al."EXACT PENALTY FUNCTION FOR \ell2,1 NORM MINIMIZATION OVER THE STIEFEL MANIFOLD".SIAM JOURNAL ON OPTIMIZATION 31.4(2021):3097-3126. |
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