三分块凸优化问题的改进Peaceman-Rachford分裂法  

An improved Peaceman-Rachford splitting method for three-block convex optimization problems

作　　者：刘学念 黄甜 LIU Xue-nian;HUANG Tian(College of Mathematics and Statistics,Hubei Normal University,Huangshi 435002,China;School of Education,Shandong Vocationd University of Foreign Affairs,Weihai 264500,China)

机构地区：[1]湖北师范大学数学与统计学院,湖北黄石435002 [2]山东外事职业大学教育学院,山东威海264500

出　　处：《湖北师范大学学报（自然科学版）》2023年第4期8-16,共9页Journal of Hubei Normal University：Natural Science

基　　金：山东外事职业大学2024年科研项目(2024ZD01)资助。

摘　　要：对于带有线性约束的三块可分凸优化问题,给出了带有Bregman距离的Peaceman-Rachford(PR)分裂法的迭代形式,并对其进行改进。然后在变分不等式的框架下研究该算法的全局收敛性,并给出了在遍历意义下O(1/t)的最坏收敛速率。For three-block separable convex optimization problems with linear constraints,this study proposes and an iterative form of the Peaceman-Rachford(PR)splitting method with Bregman distance and makes some improvement on this method.Then,it exploresthe global convergence of the algorithm under the framework of variational inequalities and gives the worst-case convergence rate of in the traversal sense.

关 键 词：凸优化 Bregman距离 变分不等式 PR分裂法 分块计算 

分 类 号：O224[理学—运筹学与控制论]