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QUADRATIC GROWTH CONDITIONS FOR CONVEX MATRIX OPTIMIZATION PROBLEMS ASSOCIATED WITH SPECTRAL FUNCTIONS
Cui, Ying1; Ding, Chao2; Zhao, Xinyuan3
2017
Source PublicationSIAM JOURNAL ON OPTIMIZATION
ISSN1052-6234
Volume27Issue:4Pages:2332-2355
AbstractIn 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.
Keywordmatrix optimization spectral functions quadratic growth conditions metric sub regularity augmented Lagrangian function fast convergence rates
DOI10.1137/17M1116325
Language英语
Funding ProjectNational 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 Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000418661400008
PublisherSIAM PUBLICATIONS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29205
Collection应用数学研究所
Affiliation1.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
Recommended Citation
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.
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