GRADIENT-BASED METHOD WITH ACTIVE SET STRATEGY FOR l(1) OPTIMIZATION

doi:10.1090/mcom/3238

	GRADIENT-BASED METHOD WITH ACTIVE SET STRATEGY FOR l(1) OPTIMIZATION
	Cheng, Wanyou 1; Dai, Yu-Hong2
	2018-05-01
发表期刊	MATHEMATICS OF COMPUTATION
ISSN	0025-5718
卷号	87 期号:311 页码:1283-1305
摘要	In this paper, we propose an identification function and develop an active set identification technique for solving the l(1) optimization problem. Such a technique has a strong ability to accurately identify the zero components in a neighbourhood of an isolated stationary point without strict complementarity conditions. Based on the active set identification technique, we propose a gradient-based method for the l(1) optimization problem. To accelerate the algorithm, a subspace Barzilai-Borwein steplength and a subspace exact steplength are developed, respectively. Under appropriate conditions, we show that the method with the nonmonotone line search technique is globally convergent. Numerical experiments with compressive sensing problems show that our approach is competitive with several known methods for the standard l(2)-l(1) problem.
关键词	l(1) minimization compressive sensing active set Barzilai-Borwein method
DOI	10.1090/mcom/3238
语种	英语
资助项目	Chinese NSF[11371154] ; Chinese NSF[11331012] ; Chinese NSF[81173633] ; Key Project of Chinese National Programs for Fundamental Research and Development[2015CB856000] ; China National Funds for Distinguished Young Scientists[11125107] ; Guangdong Province Outstanding Young Teacher Training Program[3XZ150603] ; Guangdong Province Outstanding Young Teacher Training Program[2015KTSCX1]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000425720100009
出版者	AMER MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/29588
专题	计算数学与科学工程计算研究所
通讯作者	Cheng, Wanyou
作者单位	1.Dongguan Univ Technol, Coll Comp, Dongguan 523000, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Cheng, Wanyou,Dai, Yu-Hong. GRADIENT-BASED METHOD WITH ACTIVE SET STRATEGY FOR l(1) OPTIMIZATION[J]. MATHEMATICS OF COMPUTATION,2018,87(311):1283-1305.
APA	Cheng, Wanyou,&Dai, Yu-Hong.(2018).GRADIENT-BASED METHOD WITH ACTIVE SET STRATEGY FOR l(1) OPTIMIZATION.MATHEMATICS OF COMPUTATION,87(311),1283-1305.
MLA	Cheng, Wanyou,et al."GRADIENT-BASED METHOD WITH ACTIVE SET STRATEGY FOR l(1) OPTIMIZATION".MATHEMATICS OF COMPUTATION 87.311(2018):1283-1305.