The subgradient double projection method for variational inequalities in a Hilbert space

Fixexd point theory and applications

Lian Zheng¹ 

[1] Department of Mathematics and Computer Science, Yangtze Normal University, Fuling, China

关键词: variational inequalities;    nonexpansive mapping;    subgradient;    double projection algorithm;    weak convergence;   

DOI  :  10.1186/1687-1812-2013-136

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We present a modification of the double projection algorithm proposed by Solodov and Svaiter for solving variational inequalities (VI) in a Hilbert space. The main modification is to use the subgradient of a convex function to obtain a hyperplane, and the second projection onto the intersection of the feasible set and a halfspace is replaced by projection onto the intersection of two halfspaces. In addition, we propose a modified version of our algorithm that is to find a solution of VI which is also a fixed point of a given nonexpansive mapping. We establish weak convergence theorems for our algorithms. MSC:90C25, 90C30.

【 授权许可】

CC BY