摘要
Douglas-Rachford分裂算法(DRSM)是求解两个闭凸集交的可行问题非常有效的算法。对于多个闭凸集的情形,Borwein和Tam提出了循环DRSM来求解,并证明了算法的收敛性。广义DRSM作为经典DRSM的推广,可以使得算法收敛速度更快。在本文中,我们提出使用广义循环DRSM来求解多集凸可行问题,借助均值算子的性质,我们给出了算法的收敛性。
Douglas-Rachford splitting algorithm(DRSM)is an effective algorithm for solving feasible problems of two closed convex sets intersection.In the case of multiple closed convex sets,Borwein and Tam propose a cyclic DRSM to solve it,and the convergence of the algorithm is also proved.As the generalization of classic DRSM,generalized DRSM can make the algorithm converge at a faster rate.In this paper,generalized cyclic DRSM is proposed to solve the multi set convex feasible problem.By virtue of the property of average operator,the convergence of the algorithm is given.
作者
郭科
张有才
GUO Ke;ZHANG Youcai(School of Mathematics and Information,China West Normal University,Nanchong Sichuan 637009,China)
出处
《西华师范大学学报(自然科学版)》
2018年第4期404-409,共6页
Journal of China West Normal University(Natural Sciences)
基金
国家自然科学基金资助项目(11571178)
四川省高校创新团队(16TD0019)
西华师范大学英才基金项目(17YC379)
西华师范大学科研启动基金项目(17E084)
2018年省级大学生创新创业训练计划项目(201810638047)