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GRADIENT-BASED METHOD WITH ACTIVE SET STRATEGY FOR l(1) OPTIMIZATION
Cheng, Wanyou1; Dai, Yu-Hong2
2018-05-01
Source PublicationMATHEMATICS OF COMPUTATION
ISSN0025-5718
Volume87Issue:311Pages:1283-1305
AbstractIn 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.
Keywordl(1) minimization compressive sensing active set Barzilai-Borwein method
DOI10.1090/mcom/3238
Language英语
Funding ProjectChinese 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 Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000425720100009
PublisherAMER MATHEMATICAL SOC
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29588
Collection计算数学与科学工程计算研究所
Affiliation1.Dongguan Univ Technol, Coll Comp, Dongguan 523000, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing, Peoples R China
Recommended Citation
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.
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