广义循环Douglas-Rachford算法

Generalized Cyclic Douglas-Rachford Algorithm

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.