General Iterative Methods For Finitely Many Variational Inequalities With Applications To Optimization Problems

In this paper,we introduce a general iterative method for a certain optimization problem of which the constrained set is the intersectional set of the solution set of finitely many variational inequality problems for continuous monotone mappings,the solution set of finitely many variational inclusion problems and the fixed point set of a continuous pseudocontractive mapping in a real Hilbert space.This paper consists of four chapters.Now we describe them one by one.In Chapter 1,we recall the simple history of the variational inequality theory and state the main work of this paper.In Chapter 2,we introduce the implicit iterative algorithm and its properties.In Chapter 3,under some suitable control conditions,according to the properties of the implicit iterative method,we establish the strong convergence of the proposed method to an element of the intersectional set,which is the unique solution of a certain optimization problem.As a.direct consequence,we obtain the unique minimum norm element of the intersectional set.In Chapter 4,we introduce an explicit iterative method,and also make the convergence analysis of the explicit iterative method in the same way.The results presented in this paper improve,extend and develop some recent corresponding results in the literature.