Weak convergence theorem for a class of split variational inequality problems and applications in a Hilbert space

Journal of inequalities and applications

Ming Tian¹ 

关键词: iterative method;    extragradient method;    weak convergence;    variational inequality;    monotone mapping;    equilibrium problem;    constrained convex minimization problem;    split feasibility problem;    58E35;    47H09;    65J15;   

DOI  :  10.1186/s13660-017-1397-9

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we consider the algorithm proposed in recent years by Censor, Gibali and Reich, which solves split variational inequality problem, and Korpelevich’s extragradient method, which solves variational inequality problems. As our main result, we propose an iterative method for finding an element to solve a class of split variational inequality problems under weaker conditions and get a weak convergence theorem. As applications, we obtain some new weak convergence theorems by using our weak convergence result to solve related problems in nonlinear analysis and optimization.

【 授权许可】

CC BY