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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 Publication SCIENCE CHINA-MATHEMATICS ISSN 1674-7283 Volume 62Issue:1Pages:185-204 Abstract In 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. Keyword sparse optimization non-convex approximation iterative thresholding algorithm DOI 10.1007/s11425-017-9315-9 Language 英语 Funding Project National Natural Science Foundation of China[11771275] WOS Research Area Mathematics WOS Subject Mathematics, Applied ; Mathematics WOS ID WOS:000455688300010 Publisher SCIENCE PRESS Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/32338 Collection 计算数学与科学工程计算研究所 Corresponding Author Bai, Yanqin Affiliation 1.Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China Recommended CitationGB/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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