Mixed quasi regularized variational inequalities

In this paper, we introduce and study a new class of variational inequalities, known as mixed quasi regularized variational inequality in the setting of nonconvexity. We use the auxiliary principle technique to suggest and analyze some iterative schemes for regularized variational inequalities. We prove that the convergence of these iterative methods requires either pseudomonotonicity or partially relaxed strongly monotonicity. Our proofs of convergence are very simple. As special cases, we obtain earlier results for solving general variational inequalities involving the convex sets.