Abstract
In this paper, Levitin-Polyak well-posedness for two classes ofgeneralized vector quasi-equilibrium problems is introduced.Criteria and characterizations of the Levitin-Polyak well-posednessare investigated. By virtue of gap functions for the generalizedvector quasi-equilibrium problems, some equivalent relations areobtained between the Levitin-Polyak well-posedness for optimizationproblems and the Levitin-Polyak well-posedness for generalizedvector quasi-equilibrium problems. Finally, a set-valued version ofEkeland's variational principle is derived and applied to establisha sufficient condition for Levitin-Polyak well-posedness of a classof generalized vector quasi-equilibrium problems.
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