非扩张映射及一种改进的邻近点算法的收敛性定理

Convergence Theorems for Nonexpansive Mappings and an Improved Proximal Point Algorithm

在CAT(0)空间中,为寻找三个非扩张映射的不动点集与真凸下半连续函数的极小元集的公共元,提出了一种改进的邻近点算法,然后在CAT(0)空间中研究改进的邻近点算法的收敛性,并得到了改进的邻近点算法的迭代序列{}xnΔ-收敛于非扩张映射的不动点集与真凸下半连续函数的极小元集的公共元的结论.

In order to find the common elements of the set of fixed points of three nonexpansive mappings and the minimal ele-ment of the set of a proper convex lower semi-continuous function in CAT(0)spaces,an improved proximal algorithm was pro-posed,and then the convergence of the improved neighbor algorithm was studied in CAT(0)spaces.The conclusion is obtained that the iterative sequences of the improved proximal point algorithm converges to the common elements of the set of fixed points of the nonexpansive mappings and the minimal element set of a proper convex lower semi-continuous function.