求解大规模l1问题的L-BFGS算法  

AN L-BFGS ALGORITHM FOR SOLVING LARGE-SCALE l1 PROBLEMS

作　　者：陈鸿升 叶建豪 张嘉昊 程万友 Chen Hongsheng;Ye Jianhao;Zhang Jiahao;Cheng Wanyou(College of Computer Science,Dongguan University of Technology,Dongguan 523808,China)

机构地区：[1]东莞理工学院,东莞523808

出　　处：《计算数学》2023年第3期309-320,共12页Mathematica Numerica Sinica

基　　金：国家自然科学基金(12271187,1196101011,11971106);广东省自然科学基金(2022A1515010567);广东省普通高校重点领域专项(2021ZDZX1054)资助。

摘　　要：本文提出一种求解大规模l1问题的L-BFGS算法.在积极集集合上算法的搜索方向与临界阙值算法[7,9]的方向相同,自由空间集合上使用了L-BFGS的搜索方向.在适当的条件下,我们证明了使用非单调技术的算法是全局收敛的.数值实验证明所提出的算法是有效的.In this paper,an L-BFGS algorithm for solving large-scale l problems is proposed.The search direction of the algorithm on the active set is the same as that of the ISTA[7,9],and the search direction of L-BFGS is used on the free space set.Under some appropriate conditions,we prove that the proposed algorithm with nonmonotonic techniques converges globally.Numerical experiments show that the proposed algorithm is eficient.

关 键 词：稀疏优化 临近点算法 L-BFGS 收敛性 

分 类 号：O224[理学—运筹学与控制论]