QUADRATIC GROWTH CONDITIONS FOR CONVEX MATRIX OPTIMIZATION PROBLEMS ASSOCIATED WITH SPECTRAL FUNCTIONS
文献类型：期刊论文
| 作者 | Cui, Ying1; Ding, Chao2 ; Zhao, Xinyuan3
|
| 刊名 | SIAM JOURNAL ON OPTIMIZATION
 |
| 出版日期 | 2017 |
| 卷号 | 27期号:4页码:2332-2355 |
| 关键词 | matrix optimization spectral functions quadratic growth conditions metric sub regularity augmented Lagrangian function fast convergence rates |
| ISSN号 | 1052-6234 |
| DOI | 10.1137/17M1116325 |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000418661400008 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/29204]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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