Levitin–Polyak well-posedness of split quasi-equilibrium problems

In this paper, we introduce two types of Levitin-Polyak well-posedness for split quasi-equilibrium problems. We establish different characterizations of these well-posedness notions with and without gap functions for split quasi-equilibrium problems. Furthermore, we provide equivalence between the well-posedness of constrained optimization problems and that of split quasi-equilibrium problems using gap function techniques. By analyzing the upper semicontinuity of approximate solution sets, we derive necessary and/or sufficient conditions for type I Levitin-Polyak well-posedness. Numerical examples are provided to validate our theoretical findings.