Levitin-Polyak well-posedness of variational inequalities

In this paper we consider the Levitin-Polyak well-posedness of variational inequalities. We derive a characterization of the Levitin-Polyak well-posedness by considering the size of Levitin-Polyak approximating solution sets of variational inequalities. We also show that the Levitin-Polyak well-posedness of variational inequalities is closely related to the Levitin-Polyak well-posedness of minimization problems and fixed point problems. Finally, we prove that under suitable conditions, the Levitin-Polyak well-posedness of a variational inequality is equivalent to the uniqueness and existence of its solution.