KMS Of Academy of mathematics and systems sciences, CAS
A semismooth Newton based augmented Lagrangian method for nonsmooth optimization on matrix manifolds | |
Zhou, Yuhao1; Bao, Chenglong2,3; Ding, Chao4; Zhu, Jun1 | |
2022-10-05 | |
发表期刊 | MATHEMATICAL PROGRAMMING |
ISSN | 0025-5610 |
页码 | 61 |
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. |
关键词 | Nonsmooth manifold optimization Semismooth Newton method Augmented Lagrangian method Riemannian manifold |
DOI | 10.1007/s10107-022-01898-1 |
收录类别 | SCI |
语种 | 英语 |
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 |
WOS类目 | Computer Science, Software Engineering ; Operations Research & Management Science ; Mathematics, Applied |
WOS记录号 | WOS:000864296200001 |
出版者 | SPRINGER HEIDELBERG |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/60839 |
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. |
条目包含的文件 | 条目无相关文件。 |
除非特别说明,本系统中所有内容都受版权保护,并保留所有权利。
修改评论