Efficient projected gradient methods for cardinality constrained optimization

doi:10.1007/s11425-016-9124-0

	Efficient projected gradient methods for cardinality constrained optimization
	Xu, Fengmin 1; Dai, Yuhong2 ; Zhao, Zhihu 1; Xu, Zongben 3
	2019-02-01
Source Publication	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
Volume	62 Issue:2 Pages:245-268
Abstract	Sparse 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.
Keyword	sparse approximation projected gradient method global convergence signal recovery index tracking
DOI	10.1007/s11425-016-9124-0
Language	英语
Funding Project	National 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 Area	Mathematics
WOS Subject	Mathematics, Applied ; Mathematics
WOS ID	WOS:000459419000003
Publisher	SCIENCE PRESS
Citation statistics
Document Type	期刊论文
Identifier	http://ir.amss.ac.cn/handle/2S8OKBNM/32590
Collection	计算数学与科学工程计算研究所
Corresponding Author	Dai, Yuhong
Affiliation	1.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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