摘要
本文主要回顾了单调算子理论与分裂算法的基本概念和结果，重点介绍Forward—Backward分裂算法和Douglas-Rachford分裂算法的收敛性理论及应用．同时，也介绍了这些方法处理非凸优化问题的最新进展以及一些前沿和热点问题．最后提出了几个未来可以继续研究的方向．
In this paper, we revisit the basic notations and results of monotone operator theory and splitting methods, especially for the convergence theory and its applications of the Forward- Backward splitting method and the Douglas-Rachford splitting method. Meanwhile, we present the recent advances of these methods for solving nonconvex optimization problems and some heated research areas. Last, we list several research directions for the future work.
作者
郭科
韩德仁
Guo Ke;Han Deren(School of Mathematics and Information,China West Normal University,Nanchong 637000,Chin;School of Mathematics and System Sciences,Beihang University,Beijing 100191,China)
出处
《计算数学》
CSCD
北大核心
2018年第4期418-435,共18页
Mathematica Numerica Sinica
基金
国家杰出青年科学基金(No.11625105)
国家自然科学基金项目(Nos.11801455,11571178,11431002)
西华师范大学博士科研启动基金(No.17E084)
