A splitting algorithm for finding fixed points of nonexpansive mappings and solving equilibrium problems

被引:4
作者
Le Dung Muu [1 ]
Xuan Thanh Le [2 ]
机构
[1] Thang Long Univ, Inst Math & Appl Sci, Hanoi, Vietnam
[2] Vietnam Acad Sci & Technol, Inst Math, Hanoi, Vietnam
关键词
Monotone equilibria; Fixed point; Common solution; Splitting algorithm; STRONG-CONVERGENCE THEOREMS; SUBGRADIENT ALGORITHM; MONOTONE-OPERATORS; EXISTENCE; WEAK;
D O I
10.1007/s11784-018-0612-8
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider the problem of finding a fixed point of a nonexpansive mapping, which is also a solution of a pseudo-monotone equilibrium problem, where the bifunction in the equilibrium problem is the sum of two ones. We propose a splitting algorithm combining the gradient method for equilibrium problem and the Mann iteration scheme for fixed points of nonexpansive mappings. At each iteration of the algorithm, two strongly convex subprograms are required to solve separately, one for each of the component bifunctions. Our main result states that, under paramonotonicity property of the given bifunction, the algorithm converges to a solution without any Lipschitz-type condition as well as Holder continuity of the bifunctions involved.
引用
收藏
页数:16
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