Iterative Methods And Convergence Analysis For Monotone Variational Inequalities And Fixed Point Problem

With the wide application of variational inequality theory,how to effectively solve variational inequality problems has attracted more and more attention.Therefore,it is important to develop efficient and realizable algorithm techniques for variational inequality problems.In this paper,based on Hilbert space,two problems of pseudo monotone variational inequality and fixed point,split variational inequality are studied,respectively,the two problems are analyzed and the solution algorithm are given.This paper is divided into four parts: The first part introduces the development of variational inequality,and gives the research status and significance of variational inequality.The second part studies the pseudomonotone variational inequality and fixed point problem,and proposes two algorithms: one is the modified Tseng’s algorithm,the other is the linear search self-adaptive projection algorithm,and then proves the strong convergence of the algorithm respectively.In the third part,we study the split variational inequality problem involved in an η-inverse stronglyφ-monotone operator and a pseudomonotone operator,an iterative algorithm using self-adaptive technique and Tseng’s method is proposed,and the strong convergence analysis of the algorithm is given.The fourth part is a summary of this article and a prospect of the future research direction,hoping that this kind of problem can be more popularized and applied.