SPECTRAL OPERATORS OF MATRICES: SEMISMOOTHNESS AND CHARACTERIZATIONS OF THE GENERALIZED JACOBIAN

doi:10.1137/18M1222235

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	SPECTRAL OPERATORS OF MATRICES: SEMISMOOTHNESS AND CHARACTERIZATIONS OF THE GENERALIZED JACOBIAN
	Ding, Chao1 ; Sun, Defeng 2; Sun, Jie 3; Toh, Kim-Chuan 4,5
	2020
发表期刊	SIAM JOURNAL ON OPTIMIZATION
ISSN	1052-6234
卷号	30 期号:1 页码:630-659
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.
关键词	spectral operators matrix-valued functions semismoothness generalized Jacobian
DOI	10.1137/18M1222235
收录类别	SCI
语种	英语
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
WOS类目	Mathematics, Applied
WOS记录号	WOS:000546998300024
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/51733
专题	应用数学研究所
通讯作者	Ding, Chao
作者单位	1.Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing, Peoples R China 2.Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Peoples R China 3.Curtin Univ, Fac Sci & Engn, Bentley, WA 6102, Australia 4.Natl Univ Singapore, Dept Math, Singapore, Singapore 5.Natl Univ Singapore, Inst Operat Res & Analyt, 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.