A new piecewise quadratic approximation approach for L-0 norm minimization problem
文献类型：期刊论文
| 作者 | Li, Qian1; Bai, Yanqin1; Yu, Changjun1; Yuan, Ya-xiang2
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| 刊名 | SCIENCE CHINA-MATHEMATICS
 |
| 出版日期 | 2019 |
| 卷号 | 62期号:1页码:185-204 |
| 关键词 | sparse optimization non-convex approximation iterative thresholding algorithm |
| ISSN号 | 1674-7283 |
| DOI | 10.1007/s11425-017-9315-9 |
| 英文摘要 | 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. |
| 资助项目 | National Natural Science Foundation of China[11771275] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000455688300010 |
| 出版者 | SCIENCE PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/32337]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Bai, Yanqin |
| 作者单位 | 1.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 |
| 推荐引用方式 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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