Projection Method Approach for General Regularized Non-convex Variational Inequalities

In this paper, we investigate or analyze non-convex variational inequalities and general non-convex variational inequalities. Two new classes of non-convex variational inequalities, named regularized non-convex variational inequalities and general regularized non-convex variational inequalities, are introduced, and the equivalence between these two classes of non-convex variational inequalities and the fixed point problems are established. A projection iterative method to approximate the solutions of general regularized non-convex variational inequalities is suggested. Meanwhile, the existence and uniqueness of solution for general regularized non-convex variational inequalities is proved, and the convergence analysis of the proposed iterative algorithm under certain conditions is studied.