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Dual-density-based reweighted l(1)-algorithms for a class of l(0)-minimization problems
Xu, Jialiang1; Zhao, Yun-Bin2,3
AbstractThe optimization problem with sparsity arises in many areas of science and engineering such as compressed sensing, image processing, statistical learning and data sparse approximation. In this paper, we study the dual-density-based reweighted l(1)-algorithms for a class of l(0)-minimization models which can be used to model a wide range of practical problems. This class of algorithms is based on certain convex relaxations of the reformulation of the underlying l(0)-minimization model. Such a reformulation is a special bilevel optimization problem which, in theory, is equivalent to the underlying l(0)-minimization problem under the assumption of strict complementarity. Some basic properties of these algorithms are discussed, and numerical experiments have been carried out to demonstrate the efficiency of the proposed algorithms. Comparison of numerical performances of the proposed methods and the classic reweighted l(1)-algorithms has also been made in this paper.
KeywordMerit functions for sparsity l(0)-minimization Dual-density-based algorithm Strict complementarity Bilevel optimization Convex relaxation
Indexed BySCI
Funding ProjectNational Natural Science Foundation of China[12071307] ; National Natural Science Foundation of China[11771003]
WOS Research AreaOperations Research & Management Science ; Mathematics
WOS SubjectOperations Research & Management Science ; Mathematics, Applied
WOS IDWOS:000641212300001
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Document Type期刊论文
Corresponding AuthorZhao, Yun-Bin
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Hua Loo Keng Ctr Math Sci, Beijing 100190, Peoples R China
2.Chinese Univ Hong Kong, Shenzhen Res Inst Big Data, Shenzhen, Guangdong, Peoples R China
3.Univ Birmingham, Birmingham B15 2TT, W Midlands, England
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GB/T 7714
Xu, Jialiang,Zhao, Yun-Bin. Dual-density-based reweighted l(1)-algorithms for a class of l(0)-minimization problems[J]. JOURNAL OF GLOBAL OPTIMIZATION,2021:24.
APA Xu, Jialiang,&Zhao, Yun-Bin.(2021).Dual-density-based reweighted l(1)-algorithms for a class of l(0)-minimization problems.JOURNAL OF GLOBAL OPTIMIZATION,24.
MLA Xu, Jialiang,et al."Dual-density-based reweighted l(1)-algorithms for a class of l(0)-minimization problems".JOURNAL OF GLOBAL OPTIMIZATION (2021):24.
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