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Efficient projected gradient methods for cardinality constrained optimization

文献类型：期刊论文

作者Xu, Fengmin1; Dai, Yuhong2; Zhao, Zhihu1; Xu, Zongben3
刊名SCIENCE CHINA-MATHEMATICS
出版日期2019-02-01
卷号62期号:2页码:245-268
关键词sparse approximation projected gradient method global convergence signal recovery index tracking
ISSN号1674-7283
DOI10.1007/s11425-016-9124-0
英文摘要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.
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
语种英语
WOS记录号WOS:000459419000003
出版者SCIENCE PRESS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/32589]  
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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