A class of smooth exact penalty function methods for optimization problems with orthogonality constraints

doi:10.1080/10556788.2020.1852236

CSpace

	A class of smooth exact penalty function methods for optimization problems with orthogonality constraints
	Xiao, Nachuan 1,2; Liu, Xin 1,2; Yuan, Ya-xiang 1
	2020-11-25
发表期刊	OPTIMIZATION METHODS & SOFTWARE
ISSN	1055-6788
页码	37
摘要	Updating the augmented Lagrangian multiplier by closed-form expression yields efficient first-order infeasible approach for optimization problems with orthogonality constraints. Hence, parallelization becomes tractable in solving this type of problems. Inspired by this closed-form updating scheme, we propose a novel penalty function with compact convex constraints (PenC). We show that PenC can act as an exact penalty model which shares the same global minimizers as the original problem with orthogonality constraints. Based on PenC, we first propose a first-order algorithm called PenCF and establish its global convergence and local linear convergence rate under some mild assumptions. For the case that the computation and storage of Hessian is achievable, and we pursue high precision solution and fast local convergence rate, a second-order approach called PenCS is proposed for solving PenC. To avoid expensive calculation or solving a hard subproblem in computing the Newton step, we propose a new strategy to do it approximately which still leads to quadratic convergence locally. Moreover, the main iterations of both PenCF and PenCS are orthonormalization-free and hence parallelizable. Numerical experiments illustrate that PenCF is comparable with the existing first-order methods. Furthermore, PenCS shows its stability and high efficiency in obtaining high precision solution comparing with the existing second-order methods.
关键词	Orthogonality constraint Stiefel manifold augmented Lagrangian method
DOI	10.1080/10556788.2020.1852236
收录类别	SCI
语种	英语
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	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:000592046900001
出版者	TAYLOR & FRANCIS LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52483
专题	中国科学院数学与系统科学研究院
通讯作者	Liu, Xin
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp, Beijing, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Xiao, Nachuan,Liu, Xin,Yuan, Ya-xiang. A class of smooth exact penalty function methods for optimization problems with orthogonality constraints[J]. OPTIMIZATION METHODS & SOFTWARE,2020:37.
APA	Xiao, Nachuan,Liu, Xin,&Yuan, Ya-xiang.(2020).A class of smooth exact penalty function methods for optimization problems with orthogonality constraints.OPTIMIZATION METHODS & SOFTWARE,37.
MLA	Xiao, Nachuan,et al."A class of smooth exact penalty function methods for optimization problems with orthogonality constraints".OPTIMIZATION METHODS & SOFTWARE (2020):37.