Iterative Algorithm For Solving Some Variational Inequalities In Hilbert

The main purpose of this paper is to study the iterative algorithmof some variational inequalities. This thesis is divided into three chapters.In chapter 1, we mainly introduce some pre-knowledge of variationalinequality, and we introduce the new definition ofΘ-pseudomonotone,Θ-pseudomonotone+,Θ-pseudomonotone+* andρ-strongly pseudomonotone.In chapter 2, we considered the iterative algorithm of general variationalinequalities in Hilbert spaces. In each step, we choose an appropriate pointin the set-valued mapping, followed by an orthogonal projection onto thefeasible set to get the next iterative sequence. We also prove that the sequencegenerated by this method is weakly convergent if the set-valued mapping T ispseudomonotone*.In chapter 3, we propose a projection subgradient method for solvingsome classical variational inequality problem over the set of solutions of mixedvariational inequalities. Under the conditions that T is aΘ-pseudomonotonemapping and A is aρ-strongly pseudomonotone mapping, we prove theconvergence of the algorithm constructed by projection subgradient method.