Levitin–Polyak Well-Posedness for Optimization Problems with Generalized Equilibrium Constraints

In this paper, we consider Levitin–Polyak well-posedness of parametric generalized equilibrium problems and optimization problems with generalized equilibrium constraints. Some criteria for these types of well-posedness are derived. In particular, under certain conditions, we show that generalized Levitin–Polyak well-posedness of a parametric generalized equilibrium problem is equivalent to the nonemptiness and compactness of its solution set. Finally, for an optimization problem with generalized equilibrium constraints, we also obtain that, under certain conditions, Levitin–Polyak well-posedness in the generalized sense is equivalent to the nonemptiness and compactness of its solution set.

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