Abstract
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.
Highlights
The variational inequality problem (VIP) is generated from the method of mathematical physics and nonlinear programming
In this paper, based on the work by Censor et al combined with Korpelevich’s extragradient method and Byrne’s CQ algorithm, 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
5 Conclusion It should be pointed out that the variational inequality problem and the split feasibility problem are important in nonlinear analysis and optimization
Summary
The variational inequality problem (VIP) is generated from the method of mathematical physics and nonlinear programming. It has considerable applications in many fields, such as physics, mechanics, engineering, economic decision, control theory and so on. Variational inequality is a system of partial differential equations. In , Stampacchia [ ] first introduced the VIP for modeling in the mechanics problem. The VIP was generated from mathematical physics equations early on because the Lax-Milgram theorem was extended from the Hilbert space to its nonempty closed convex subset, so we got the first existence and uniqueness theorem of VIP. In the s, the VIP became more and more important in nonlinear analysis and optimization problem
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