一个求解绝对值方程组稀疏解问题的不动点算法  

A Fixed-point Algorithm for the Sparest Solution Problem of Absolute Value Equations

作　　者：王鹏 任天 Wang Peng;Ren Tian(School of Mathematical Science,Tianjin University,Tianjin 30035)

机构地区：[1]天津大学数学学院,天津300354

出　　处：《首都师范大学学报（自然科学版）》2018年第4期22-26,共5页Journal of Capital Normal University：Natural Science Edition

摘　　要：本文提出基于prox算子不动点算法(fixed-point algorithm)求解NP难的绝对值方程组Ax-x=b的最稀疏解.该算法首先将问题松弛为l1范数最小化问题,利用外罚函数法进一步松弛为一个无约束优化问题,其次求解近似后的无约束优化问题.In this paper,the prox operator based on the fixed point algorithm was proposed in order to solve the sparsest solution of the NP-hard absolute value equations Ax-｜ x ｜ = b. The algorithm first relaxed the question to a l1-norm minimization problem,it was further relaxed to an unconstrained optimization problem by exterior penalty function method,next the fixed-point algorithm of the prox operator was used to solve the approximate optimization problem.

关 键 词：l1范数最小化 稀疏解 prox算子 绝对值方程组 

分 类 号：O221.2[理学—运筹学与控制论]