A new piecewise quadratic approximation approach for L_0 norm minimization problem

作     者：Qian Li Yanqin Bai Changjun Yu Ya-xiang Yuan 

作者机构：Department of MathematicsShanghai University Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of Sciences 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2019年第62卷第1期

页      面：185-204页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by National Natural Science Foundation of China (Grant No. 11771275) 

主　　题：sparse optimization non-convex approximation iterative thresholding algorithm 

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 piecewis, quadratic function to approximate the L_0 ***, 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.