求解l_(1)问题的积极集临近牛顿算法  

AN ACTIVE SET PROXIMAL NEWTON METHOD FOR l_(1) OPTIMIZATION

作　　者：林彭壮汉 李凯 程万友 Linpeng Zhuanghan;Li Kai;Cheng Wanyou(College of Computer Science,Dongguan University Of Technology,Dongguan 523808,Chin)

机构地区：[1]东莞理工学院,东莞523808

出　　处：《数值计算与计算机应用》2023年第4期409-419,共11页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(12271187,11961011,11971106);广东省自然科学基金(2022A1515010567);广东省教育厅高校重点基金(2021ZDZX1054)资助.

摘　　要：本文提出一种基于积极集识别技术的临近牛顿算法用以求解l_(1)问题.该方法的一个优势在于利用了ISTA算法良好的支集辨认性质去确定自由变量和积极集变量,另一个优势在于利用了部分Hessian矩阵的信息去更新自由变量。在适当的条件下,我们证明了所提出的算法在使用非单调线搜索策略情况下是全局收敛的.数值实验证明提出的算法是有效的.In this paper,based on the active set identification,we propose a Proximal Newton method for l_(1) problems.One advantage of this method is that it uses the good support identification property of the ISTA algorithm to determine the free variables and active set variables,and another advantage is that it uses the information of the partial Hessian matrix to update the free variables.Under appropriate conditions,we demonstrate the global convergence of the algorithm with a nonmonotonic line search strategy.The results of numerical experiments show that our proposed algorithm is effective.

关 键 词：稀疏优化 临近牛顿算法 积极集 收敛性 

分 类 号：O224[理学—运筹学与控制论]