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A new piecewise quadratic approximation approach for L-0 norm minimization problem
Li, Qian1; Bai, Yanqin1; Yu, Changjun1; Yuan, Ya-xiang2
2019
Source PublicationSCIENCE CHINA-MATHEMATICS
ISSN1674-7283
Volume62Issue:1Pages:185-204
AbstractIn this paper, we consider the problem of finding sparse solutions for underdetermined systems of linear equations, which can be formulated as a class of L-0 norm minimization problem. By using the least absolute residual approximation, we propose a new piecewise quadratic function to approximate the L-0 norm. Then, we develop a piecewise quadratic approximation (PQA) model where the objective function is given by the summation of a smooth non-convex component and a non-smooth convex component. To solve the (PQA) model, we present an algorithm based on the idea of the iterative thresholding algorithm and derive the convergence and the convergence rate. Finally, we carry out a series of numerical experiments to demonstrate the performance of the proposed algorithm for (PQA). We also conduct a phase diagram analysis to further show the superiority of (PQA) over L-1 and L-1/2 regularizations.
Keywordsparse optimization non-convex approximation iterative thresholding algorithm
DOI10.1007/s11425-017-9315-9
Language英语
Funding ProjectNational Natural Science Foundation of China[11771275]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000455688300010
PublisherSCIENCE PRESS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/32338
Collection计算数学与科学工程计算研究所
Affiliation1.Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Li, Qian,Bai, Yanqin,Yu, Changjun,et al. A new piecewise quadratic approximation approach for L-0 norm minimization problem[J]. SCIENCE CHINA-MATHEMATICS,2019,62(1):185-204.
APA Li, Qian,Bai, Yanqin,Yu, Changjun,&Yuan, Ya-xiang.(2019).A new piecewise quadratic approximation approach for L-0 norm minimization problem.SCIENCE CHINA-MATHEMATICS,62(1),185-204.
MLA Li, Qian,et al."A new piecewise quadratic approximation approach for L-0 norm minimization problem".SCIENCE CHINA-MATHEMATICS 62.1(2019):185-204.
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