一种带有不定性邻近项的广义Peaceman-Rachford分裂法  

A Generalized Peaceman-Rachford Splitting Method with Indefinite Proximal Term

作　　者：马龙 彭建文 MA Long;PENG Jianwen(School of Mathematics Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《应用数学》2020年第2期423-435,共13页Mathematica Applicata

基　　金：重庆市基础科学与前沿技术研究(重点)(NO.cstc2015jcyjBX0029);国家自然科学基金面上项目(11171363)。

摘　　要：针对带有线性约束的可分离凸优化问题,提出一种带有不定邻近项的广义Peaceman-Rachford(PR)分裂法.在较弱假设条件下,证明该算法迭代序列的全局收敛性和建立起在遍历情况下的最坏O(1/t)收敛速率.最后,通过数值实验验证了所提算法的有效性.To deal with the separable convex optimization problems with linear constraints,a generalized Peaceman-Rachford(PR)splitting method with indefinite proximal term is proposed.Under certain weak assumptions,the global convergence of the iterative sequence generated by the proposed algorithm is proved,and the worst-case O(1/t)convergence rate in the ergodic sense is established.Finally,the effectiveness of the proposed algorithm is proved in numerical experiments.

关 键 词：凸优化 Peaceman-Rachford分裂法 不定邻近项 

分 类 号：O224[理学—运筹学与控制论]