Two Kinds Of Projection Shrinkage Algorithm Of Solving Monotone Variational Inequality

Projection and contraction method is an important algorithm for solving variational inequalities. Based on the existing projection and contraction methods, this paper presents two new algorithms which need twice projections. We can prove it is convergent when the operator is monotonic. This paper consists of the following several parts:The first chapter introduces the relationship between the variational inequalities and optimization, nonlinear complementarity problems. And we also introduce conditions for the existence and uniqueness of the solution of variational inequalities. Finally we present some basic definitions in this chapter.In the second chapter we summarize some basic properties and related definitions which will be used in the following discussions. Then we obtain the first new algorithm of this paper through twice projections and analyze the convergence of the algorithm. At last, we use a numerical experiment to show the algorithm is effective.In the third chapter we give a new improved projection and contraction algorithm by changing the feasible direction of the old algorithm. Then we prove the new algorithm is globally convergent and show its effectiveness through an example.