Some new aspects of nonconvex inverse variational inequalities

Some new classes of nonconvex inverse variational inequalities are considered and studied. Using the projection technique, we establish the equivalence between the nonconvex inverse variational inequalities and the fixed point problems. This alternative equivalent formulation is used to study the existence of a solution of the nonconvex inverse variational inequalities. Several techniques including the projection, auxiliary principle, dynamical systems and nonexpansive mappings are explored for computing the approximate solution of nonconvex inverse variational inequalities. Convergence criteria of the proposed hybrid multi-step methods is investigated under suitable conditions. Our method of proofs is very simple as compared with other techniques. Some special cases are pointed are pointed as applications of the results. It is an open problem to explore the applications of the nonconvex inverse variational inequalities in various fields of mathematical and engineering sciences.