Levitin–Polyak well‐posedness by perturbations of inverse variational inequalities

The purpose of this paper is to investigate Levitin–Polyak type well‐posedness for inverse variational inequalities. We establish some metric characterizations of Levitin–Polyak α‐well‐posedness by perturbations. Under suitable conditions, we prove that Levitin–Polyak well‐posedness by perturbations of an inverse variational inequality is equivalent to the existence and uniqueness of its solution. Moreover, we show that Levitin–Polyak well‐posedness by perturbations of an inverse variational inequality is equivalent to Levitin–Polyak well‐posedness by perturbations of an enlarged classical variational inequality.