Projection methods for nonconvex variational inequalities

In this paper, we introduce and consider a new class of variational inequalities, which is called the nonconvex variational inequalities. We establish the equivalence between the nonconvex variational inequalities and the fixed-point problems using the projection technique. This equivalent formulation is used to discuss the existence of a solution of the nonconvex variational inequalities. We also use this equivalent alternative formulation to suggest and analyze a new iterative method for solving the nonconvex variational inequalities. We also discuss the convergence of the iterative method under suitable conditions. Our method of proof is very simple as compared with other techniques.