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

doi:10.1090/mcom/3238

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 计算数学与科学工程计算研究所

	GRADIENT-BASED METHOD WITH ACTIVE SET STRATEGY FOR l(1) OPTIMIZATION
	Cheng, Wanyou 1; Dai, Yu-Hong2
刊名	MATHEMATICS OF COMPUTATION
	2018-05-01
卷号	87 期号:311 页码:1283-1305
关键词	l(1) minimization compressive sensing active set Barzilai-Borwein method
ISSN号	0025-5718
DOI	10.1090/mcom/3238
英文摘要	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.
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
语种	英语
出版者	AMER MATHEMATICAL SOC
WOS记录号	WOS:000425720100009
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/29587]
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.