Levitin–Polyak well-posedness for parametric quasivariational inequality problem of the Minty type

In this paper, we introduce the notions of Levitin–Polyak (LP) well-posedness and Levitin–Polyak well-posedness in the generalized sense, for a parametric quasivariational inequality problem of the Minty type. Metric characterizations of LP well-posedness and generalized LP well-posedness, in terms of the approximate solution sets are presented. A parametric gap function for the quasivariational inequality problem is introduced and an equivalence relation between LP well-posedness of the parametric quasivariational inequality problem and that of the related optimization problem is obtained.