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

doi:10.1137/18M1222235

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 应用数学研究所

	SPECTRAL OPERATORS OF MATRICES: SEMISMOOTHNESS AND CHARACTERIZATIONS OF THE GENERALIZED JACOBIAN
	Ding, Chao 2; Sun, Defeng 3; Sun, Jie 4; Toh, Kim-Chuan 1,5
刊名	SIAM JOURNAL ON OPTIMIZATION
	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
出版者	SIAM PUBLICATIONS
WOS记录号	WOS:000546998300024
内容类型	期刊论文
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, Dept Math, 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, 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.