A new piecewise quadratic approximation approach for L-0 norm minimization problem

doi:10.1007/s11425-017-9315-9

	A new piecewise quadratic approximation approach for L-0 norm minimization problem
	Li, Qian 1; Bai, Yanqin 1; Yu, Changjun 1; Yuan, Ya-xiang2
	2019
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	62 期号:1 页码:185-204
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.
关键词	sparse optimization non-convex approximation iterative thresholding algorithm
DOI	10.1007/s11425-017-9315-9
语种	英语
资助项目	National Natural Science Foundation of China[11771275]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000455688300010
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/32338
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.