QUADRATIC GROWTH CONDITIONS FOR CONVEX MATRIX OPTIMIZATION PROBLEMS ASSOCIATED WITH SPECTRAL FUNCTIONS

doi:10.1137/17M1116325

CSpace > 应用数学研究所

	QUADRATIC GROWTH CONDITIONS FOR CONVEX MATRIX OPTIMIZATION PROBLEMS ASSOCIATED WITH SPECTRAL FUNCTIONS
	Cui, Ying 1; Ding, Chao2 ; Zhao, Xinyuan 3
	2017
发表期刊	SIAM JOURNAL ON OPTIMIZATION
ISSN	1052-6234
卷号	27 期号:4 页码:2332-2355
摘要	In this paper, we provide two types of sufficient conditions for ensuring the quadratic growth conditions of a class of constrained convex symmetric and nonsymmetric matrix optimization problems regularized by nonsmooth spectral functions. These sufficient conditions are derived via the study of the C-2-cone reducibility of spectral functions and the metric subregularity of their subdifferentials, respectively. As an application, we demonstrate how quadratic growth conditions are used to guarantee the desirable fast convergence rates of the augmented Lagrangian methods (ALM) for solving convex matrix optimization problems. Numerical experiments on an easy-to implement ALM applied to the fastest mixing Markov chain problem are also presented to illustrate the significance of the obtained results.
关键词	matrix optimization spectral functions quadratic growth conditions metric sub regularity augmented Lagrangian function fast convergence rates
DOI	10.1137/17M1116325
语种	英语
资助项目	National Natural Science Foundation of China[11671387] ; National Natural Science Foundation of China[11531014] ; Youth Program of the National Natural Science Foundation of China[11101016]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000418661400008
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/29205
专题	应用数学研究所
通讯作者	Cui, Ying
作者单位	1.Natl Univ Singapore, Dept Math, Singapore, Singapore 2.Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing, Peoples R China 3.Beijing Univ Technol, Beijing Inst Sci & Engn Comp, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Cui, Ying,Ding, Chao,Zhao, Xinyuan. QUADRATIC GROWTH CONDITIONS FOR CONVEX MATRIX OPTIMIZATION PROBLEMS ASSOCIATED WITH SPECTRAL FUNCTIONS[J]. SIAM JOURNAL ON OPTIMIZATION,2017,27(4):2332-2355.
APA	Cui, Ying,Ding, Chao,&Zhao, Xinyuan.(2017).QUADRATIC GROWTH CONDITIONS FOR CONVEX MATRIX OPTIMIZATION PROBLEMS ASSOCIATED WITH SPECTRAL FUNCTIONS.SIAM JOURNAL ON OPTIMIZATION,27(4),2332-2355.
MLA	Cui, Ying,et al."QUADRATIC GROWTH CONDITIONS FOR CONVEX MATRIX OPTIMIZATION PROBLEMS ASSOCIATED WITH SPECTRAL FUNCTIONS".SIAM JOURNAL ON OPTIMIZATION 27.4(2017):2332-2355.