EXACT PENALTY FUNCTION FOR \ell2,1 NORM MINIMIZATION OVER THE STIEFEL MANIFOLD
文献类型：期刊论文
| 作者 | Xiao, Nachuan1,2; Liu, Xin1,2; Ya-Xiang Yuan1 |
| 刊名 | SIAM JOURNAL ON OPTIMIZATION
 |
| 出版日期 | 2021 |
| 卷号 | 31期号:4页码:3097-3126 |
| 关键词 | orthogonality constraint Stiefel manifold nonsmooth optimization augmented Lagrangian method |
| ISSN号 | 1052-6234 |
| DOI | 10.1137/20M1354313 |
| 英文摘要 | \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. |
| 资助项目 | 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研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000738355700024 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/59835]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Xiao, Nachuan |
| 作者单位 | 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 |
| 推荐引用方式 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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