Two Classes Of Iterative Algorithms For Solving Variational Inequalities And Applications

In this paper,two classes of iterative algorithms for solving variational inequalities are introduced in Hilbert space.In order to solve the problem of variational inequalities,we improved the iterative algorithms,such as the extra-gradient method,the relaxation viscous iteration algorithms and the fastest descent method in the previous iterative.The convergence of the modified iterative algorithm is analyzed.Our results are improved and added to the corresponding results in the previous iterative.This article is divided into four parts.In the first chapter,the development status of variational inequalities is introduced.The main results and structural arrangements of this paper are also described.The first kind of iterative algorithm is introduced in the second chapter.Under suitable conditions,the weak convergence of the algorithm is proved.In the third chapter,second kinds of iterative algorithms are studied.And the proof of its convergence is given.The fourth part is the conclusion and the prospect.