文献类型：期刊文献

英文题名：Global Convergence Guarantees of (A)GIST for a Family of Nonconvex Sparse Learning Problems

作者：Zhang, Hengmin[1,2];Qian, Feng[1,2];Shang, Fanhua[3,4];Du, Wenli[1,2];Qian, Jianjun[5,6];Yang, Jian[5,6]

机构：[1]East China Univ Sci & Technol, Sch Informat Sci & Engn, Key Lab Adv Control & Optimizat Chem Proc, Minist Educ, Shanghai 200237, Peoples R China;[2]Tongji Univ, Shanghai Inst Intelligent Sci & Technol, Shanghai 200092, Peoples R China;[3]Xidian Univ, Sch Artificial Intelligence, Minist Educ, Key Lab Intelligent Percept & Image Understanding, Xian 710071, Peoples R China;[4]Peng Cheng Lab, Shenzhen 518066, Peoples R China;[5]Nanjing Univ Sci & Technol, PCA Lab, Key Lab Intelligent Percept & Syst High Dimens In, Minist Educ, Nanjing 210094, Peoples R China;[6]Nanjing Univ Sci & Technol, Sch Comp Sci & Engn, Jiangsu Key Lab Image & Video Understanding Socia, Nanjing 210094, Peoples R China

年份：2022

卷号：52

期号：5

起止页码：3276

外文期刊名：IEEE TRANSACTIONS ON CYBERNETICS

收录：;EI(收录号：20222312200162);WOS:【SCI-EXPANDED(收录号:WOS:000798227800060)】；

基金：This work was supported in part by the National Natural Science Foundation of China (Basic Science Center Program) under Grant 61988101; in part by the Program for Changjiang Scholars; in part by the National Natural Science Fund for Distinguished Young Scholars under Grant 61725301; in part by the National Natural Science Foundation of China (Major Program) under Grant 61590923; in part by the National Science Fund of China under Grant U1713208, Grant 61876083, Grant 61876220, Grant 61703163, and Grant 61906067; and in part by the China Postdoctoral Science Foundation under Grant 2019M651415.

语种：英文

外文关键词：Convergence guarantees; Kurdyka-Lojasiewica (KL) property; nonconvex sparse learning problems; optimization algorithms

摘要：In recent years, most of the studies have shown that the generalized iterated shrinkage thresholdings (GISTs) have become the commonly used first-order optimization algorithms in sparse learning problems. The nonconvex relaxations of the l(0)-norm usually achieve better performance than the convex case (e.g., l(1)-norm) since the former can achieve a nearly unbiased solver. To increase the calculation efficiency, this work further provides an accelerated GIST version, that is, AGIST, through the extrapolation-based acceleration technique, which can contribute to reduce the number of iterations when solving a family of nonconvex sparse learning problems. Besides, we present the algorithmic analysis, including both local and global convergence guarantees, as well as other intermediate results for the GIST and AGIST, denoted as (A)GIST, by virtue of the Kurdyka-Lojasiewica (KL) property and some milder assumptions. Numerical experiments on both synthetic data and real-world databases can demonstrate that the convergence results of objective function accord to the theoretical properties and nonconvex sparse learning methods can achieve superior performance over some convex ones.