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
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	62 期号:2 页码:245-268
摘要	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.
关键词	sparse approximation projected gradient method global convergence signal recovery index tracking
DOI	10.1007/s11425-016-9124-0
语种	英语
资助项目	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研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000459419000003
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/32590
专题	计算数学与科学工程计算研究所
通讯作者	Dai, Yuhong
作者单位	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
推荐引用方式 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.