ITERATIVE METHODS FOR GENERAL NONCONVEX VARIATIONAL INEQUALITIES

Abstract

In this paper, we introduce and consider some new classes of variational inequalities and the Wiener-Hopf equations. Using the projection technique, we establish the equivalence between the general nonconvex variational inequalities and the fixed point problems as well as the Wiener-Hopf equations. This alternative equivalent formulation is used to study the existence of a solution of the general convex variational inequalities. This equivalence is used to suggest and analyzed several projection iterative methods for solving the general nonconvex variational inequalities. Convergence criteria of these new iterative is also discussed under suitable conditions. Our method of proofs is very simple as compared with other techniques.