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.