SPECTRAL OPERATORS OF MATRICES: SEMISMOOTHNESS AND CHARACTERIZATIONS OF THE GENERALIZED JACOBIAN
文献类型：期刊论文
| 作者 | Ding, Chao2 ; Sun, Defeng3; Sun, Jie4; Toh, Kim-Chuan1,5
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| 刊名 | SIAM JOURNAL ON OPTIMIZATION
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| 出版日期 | 2020 |
| 卷号 | 30期号:1页码:630-659 |
| 关键词 | spectral operators matrix-valued functions semismoothness generalized Jacobian |
| ISSN号 | 1052-6234 |
| DOI | 10.1137/18M1222235 |
| 英文摘要 | Spectral operators of matrices proposed recently in [C. Ding, D. F. Sun, J. Sun, and K. C. Toh, Math. Program., 168 (2018), pp. 509-531] are a class of matrix-valued functions, which map matrices to matrices by applying a vector-to-vector function to all eigenvalues/singular values of the underlying matrices. Spectral operators play a crucial role in the study of various applications involving matrices such as matrix optimization problems that include semidefinite programming as one of most important example classes. In this paper, we will study more fundamental first- and second-order properties of spectral operators, including the Lipschitz continuity, rho-order B(ouligand)-differentiability (0 < rho <= 1), rho-order G-semismoothness (0 < rho <= 1), and characterization of generalized Jacobians. |
| 资助项目 | National Natural Science Foundation of China[11671387] ; National Natural Science Foundation of China[11531014] ; National Natural Science Foundation of China[11688101] ; Hong Kong Polytechnic University |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000546998300024 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/51732]  |
| 专题 | 应用数学研究所 |
| 通讯作者 | Ding, Chao |
| 作者单位 | 1.Natl Univ Singapore, Inst Operat Res & Analyt, Singapore, Singapore 2.Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing, Peoples R China 3.Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Peoples R China 4.Curtin Univ, Fac Sci & Engn, Bentley, WA 6102, Australia 5.Natl Univ Singapore, Dept Math, Singapore, Singapore |
| 推荐引用方式 GB/T 7714 | Ding, Chao,Sun, Defeng,Sun, Jie,et al. SPECTRAL OPERATORS OF MATRICES: SEMISMOOTHNESS AND CHARACTERIZATIONS OF THE GENERALIZED JACOBIAN[J]. SIAM JOURNAL ON OPTIMIZATION,2020,30(1):630-659. |
| APA | Ding, Chao,Sun, Defeng,Sun, Jie,&Toh, Kim-Chuan.(2020).SPECTRAL OPERATORS OF MATRICES: SEMISMOOTHNESS AND CHARACTERIZATIONS OF THE GENERALIZED JACOBIAN.SIAM JOURNAL ON OPTIMIZATION,30(1),630-659. |
| MLA | Ding, Chao,et al."SPECTRAL OPERATORS OF MATRICES: SEMISMOOTHNESS AND CHARACTERIZATIONS OF THE GENERALIZED JACOBIAN".SIAM JOURNAL ON OPTIMIZATION 30.1(2020):630-659. |
入库方式： OAI收割
来源：数学与系统科学研究院
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