A semismooth Newton based augmented Lagrangian method for nonsmooth optimization on matrix manifolds

doi:10.1007/s10107-022-01898-1

	A semismooth Newton based augmented Lagrangian method for nonsmooth optimization on matrix manifolds
	Zhou, Yuhao 1; Bao, Chenglong 2,3; Ding, Chao 4; Zhu, Jun 1
刊名	MATHEMATICAL PROGRAMMING
	2022-10-05
页码	61
关键词	Nonsmooth manifold optimization Semismooth Newton method Augmented Lagrangian method Riemannian manifold
ISSN号	0025-5610
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
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/60838]
专题	中国科学院数学与系统科学研究院
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.