Spectral operators of matrices

doi:10.1007/s10107-017-1162-3

CSpace > 应用数学研究所

	Spectral operators of matrices
	Ding, Chao1 ; Sun, Defeng 2,3; Sun, Jie 4; Toh, Kim-Chuan 5
	2018-03-01
发表期刊	MATHEMATICAL PROGRAMMING
ISSN	0025-5610
卷号	168 期号:1-2 页码:509-531
摘要	The class of matrix optimization problems (MOPs) has been recognized in recent years to be a powerful tool to model many important applications involving structured low rank matrices within and beyond the optimization community. This trend can be credited to some extent to the exciting developments in emerging fields such as compressed sensing. The Lowner operator, which generates a matrix valued function via applying a single-variable function to each of the singular values of a matrix, has played an important role for a long time in solving matrix optimization problems. However, the classical theory developed for the Lowner operator has become inadequate in these recent applications. The main objective of this paper is to provide necessary theoretical foundations from the perspectives of designing efficient numerical methods for solving MOPs. We achieve this goal by introducing and conducting a thorough study on a new class of matrix valued functions, coined as spectral operators of matrices. Several fundamental properties of spectral operators, including the well-definedness, continuity, directional differentiability and Fr,chet-differentiability are systematically studied.
关键词	Spectral operators Directional differentiability Frechet differentiability Matrix valued functions Proximal mappings
DOI	10.1007/s10107-017-1162-3
语种	英语
资助项目	National Natural Science Foundation of China[11301515] ; National Natural Science Foundation of China[11671387] ; National Natural Science Foundation of China[11531014]
WOS研究方向	Computer Science ; Operations Research & Management Science ; Mathematics
WOS类目	Computer Science, Software Engineering ; Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000426071000020
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/29637
专题	应用数学研究所
通讯作者	Sun, Defeng
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing, Peoples R China 2.Natl Univ Singapore, Dept Math, Singapore, Singapore 3.Natl Univ Singapore, Risk Management Inst, Singapore, Singapore 4.Curtin Univ, Dept Math & Stat, Bentley, WA, 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[J]. MATHEMATICAL PROGRAMMING,2018,168(1-2):509-531.
APA	Ding, Chao,Sun, Defeng,Sun, Jie,&Toh, Kim-Chuan.(2018).Spectral operators of matrices.MATHEMATICAL PROGRAMMING,168(1-2),509-531.
MLA	Ding, Chao,et al."Spectral operators of matrices".MATHEMATICAL PROGRAMMING 168.1-2(2018):509-531.