中国科学院机构知识库网格
Chinese Academy of Sciences Institutional Repositories Grid
Spectral operators of matrices

文献类型:期刊论文

作者Ding, Chao1; Sun, Defeng2,3; Sun, Jie4; Toh, Kim-Chuan5
刊名MATHEMATICAL PROGRAMMING
出版日期2018-03-01
卷号168期号:1-2页码:509-531
关键词Spectral operators Directional differentiability Frechet differentiability Matrix valued functions Proximal mappings
ISSN号0025-5610
DOI10.1007/s10107-017-1162-3
英文摘要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.
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
语种英语
WOS记录号WOS:000426071000020
出版者SPRINGER HEIDELBERG
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/29636]  
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.

入库方式: OAI收割

来源:数学与系统科学研究院

浏览0
下载0
收藏0
其他版本

除非特别说明,本系统中所有内容都受版权保护,并保留所有权利。