Properties and Iterative Methods for the Lasso and Its Variants

作     者：Hong-Kun XU 

作者机构：Department of Applied Mathematics National Sun Yat-Sen University Department of Mathematics King Abdulaziz University 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2014年第35卷第3期

页      面：501-518页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：supported by NSC 102-2115-M-110-001-MY3 

主　　题：Lasso Elastic net Smooth-lasso l1 regulaxization Sparsity Proximalmethod Dual method Projection Thresholding 

摘      要：The lasso of Tibshirani （1996） is a least-squares problem regularized by the l1 norm. Due to the sparseness promoting property of the l1 norm, the lasso has been received much attention in recent years. In this paper some basic properties of the lasso and two variants of it are exploited. Moreover, the proximal method and its variants such as the relaxed proximal algorithm and a dual method for solving the lasso by iterative algorithms are presented.