分裂可行问题的1-范数正则化方法  

The 1-Norm Regularization Method for the Split Feasibility Problem

作　　者：于海[1] 詹婉荣[1] YU Hai;ZHAN Wan-rong(School of Mathematical Sciences,Luoyang Normal University,Luoyang 471934,China)

机构地区：[1]洛阳师范学院数学科学学院,河南洛阳471934

出　　处：《数学的实践与认识》2022年第11期180-188,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11971216,62072222);河南省高等学校重点科研项目(20A110029)。

摘　　要：主要研究了分裂可行问题的1-范数正则化.首先利用1-范数正则化方法,将分裂可行问题转化为无约束优化问题.其次讨论了1-范数正则化解的若干性质,并给出了求解1-范数正则化解的邻近梯度算法.最后通过数值试验验证了算法的可行性和有效性.In this paper,we mainly study the 1-norm regularization of the split feasibility problem.Firstly,the split feasibility problem is transformed into unconstrained optimization problem by using the 1-norm regularization method.Secondly,some properties of 1-norm regularization solution are discussed,and the proximal gradient algorithm for solving 1-norm regularization solution is given.Finally,the feasibility and effectiveness of the proposed algorithm are verified by numerical experiments.

关 键 词：分裂可行问题 正则化 邻近梯度算法 稀疏 

分 类 号：O224[理学—运筹学与控制论]