A semismooth Newton based augmented Lagrangian method for nonsmooth optimization on matrix manifolds
文献类型：期刊论文
| 作者 | Zhou, Yuhao1; Bao, Chenglong2,3; Ding, Chao4 ; Zhu, Jun1
|
| 刊名 | MATHEMATICAL PROGRAMMING
 |
| 出版日期 | 2022-10-05 |
| 页码 | 61 |
| ISSN号 | 0025-5610 |
| 关键词 | Nonsmooth manifold optimization Semismooth Newton method Augmented Lagrangian method Riemannian manifold |
| DOI | 10.1007/s10107-022-01898-1 |
| 英文摘要 | This paper is devoted to studying an augmented Lagrangian method for solving a class of manifold optimization problems, which have nonsmooth objective functions and nonlinear constraints. Under the constant positive linear dependence condition on manifolds, we show that the proposed method converges to a stationary point of the nonsmooth manifold optimization problem. Moreover, we propose a globalized semismooth Newton method to solve the augmented Lagrangian subproblem on manifolds efficiently. The local superlinear convergence of the manifold semismooth Newton method is also established under some suitable conditions. We also prove that the semismoothness on submanifolds can be inherited from that in the ambient manifold. Finally, numerical experiments on compressed modes and (constrained) sparse principal component analysis illustrate the advantages of the proposed method. |
| 资助项目 | National Natural Science Foundation of China[12071464] ; Tsinghua University Initiative Scientific Research Program ; Beijing Natural Science Foundation[Z190002] |
| WOS研究方向 | Computer Science ; Operations Research & Management Science ; Mathematics |
| 语种 | 英语 |
| 出版者 | SPRINGER HEIDELBERG |
| WOS记录号 | WOS:000864296200001 |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/60838]  |
| 专题 | 应用数学研究所 |
| 通讯作者 | Bao, Chenglong |
| 作者单位 | 1.Tsinghua Univ, Dept Comp Sci & Technol, Beijing, Peoples R China 2.Tsinghua Univ, Yau Math Sci Ctr, Beijing, Peoples R China 3.Yanqi Lake Beijing Inst Math Sci & Applicat, Beijing, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing, Peoples R China |
| 推荐引用方式 GB/T 7714 | Zhou, Yuhao,Bao, Chenglong,Ding, Chao,et al. A semismooth Newton based augmented Lagrangian method for nonsmooth optimization on matrix manifolds[J]. MATHEMATICAL PROGRAMMING,2022:61. |
| APA | Zhou, Yuhao,Bao, Chenglong,Ding, Chao,&Zhu, Jun.(2022).A semismooth Newton based augmented Lagrangian method for nonsmooth optimization on matrix manifolds.MATHEMATICAL PROGRAMMING,61. |
| MLA | Zhou, Yuhao,et al."A semismooth Newton based augmented Lagrangian method for nonsmooth optimization on matrix manifolds".MATHEMATICAL PROGRAMMING (2022):61. |
入库方式： OAI收割
来源：数学与系统科学研究院
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