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Efficient projected gradient methods for cardinality constrained optimization
Xu, Fengmin1; Dai, Yuhong2; Zhao, Zhihu1; Xu, Zongben3
2019-02-01
Source PublicationSCIENCE CHINA-MATHEMATICS
ISSN1674-7283
Volume62Issue:2Pages:245-268
AbstractSparse optimization has attracted increasing attention in numerous areas such as compressed sens-ing, financial optimization and image processing. In this paper, we first consider a special class of cardinality constrained optimization problems, which involves box constraints and a singly linear constraint. An effcient approach is provided for calculating the projection over the feasibility set after a careful analysis on the projec- tion subproblem. Then we present several types of projected gradient methods for a general class of cardinality constrained optimization problems. Global convergence of the methods is established under suitable assump- tions. Finally, we illustrate some applications of the proposed methods for signal recovery and index tracking. Especially for index tracking, we propose a new model subject to an adaptive upper bound on the sparse portfo-lio weights. The computational results demonstrate that the proposed projected gradient methods are effcient in terms of solution quality.
Keywordsparse approximation projected gradient method global convergence signal recovery index tracking
DOI10.1007/s11425-016-9124-0
Language英语
Funding ProjectNational Natural Science Foundation of China[11571271] ; National Natural Science Foundation of China[11631013] ; National Natural Science Foundation of China[11331012] ; National Natural Science Foundation of China[71331001] ; National Science Fund for Distinguished Young Scholars[11125107] ; National 973 Program of China[2015CB856002] ; National 973 Program of China[2013CB329404]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000459419000003
PublisherSCIENCE PRESS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/32590
Collection计算数学与科学工程计算研究所
Affiliation1.Xi An Jiao Tong Univ, Sch Econ & Finance, Xian 710061, Shaanxi, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
3.Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China
Recommended Citation
GB/T 7714
Xu, Fengmin,Dai, Yuhong,Zhao, Zhihu,et al. Efficient projected gradient methods for cardinality constrained optimization[J]. SCIENCE CHINA-MATHEMATICS,2019,62(2):245-268.
APA Xu, Fengmin,Dai, Yuhong,Zhao, Zhihu,&Xu, Zongben.(2019).Efficient projected gradient methods for cardinality constrained optimization.SCIENCE CHINA-MATHEMATICS,62(2),245-268.
MLA Xu, Fengmin,et al."Efficient projected gradient methods for cardinality constrained optimization".SCIENCE CHINA-MATHEMATICS 62.2(2019):245-268.
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