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Levitin-Polyak well-posedness of generalized vector quasi-equilibrium problems

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  • In this paper, Levitin-Polyak well-posedness for two classes of generalized vector quasi-equilibrium problems is introduced. Criteria and characterizations of the Levitin-Polyak well-posedness are investigated. By virtue of gap functions for the generalized vector quasi-equilibrium problems, some equivalent relations are obtained between the Levitin-Polyak well-posedness for optimization problems and the Levitin-Polyak well-posedness for generalized vector quasi-equilibrium problems. Finally, a set-valued version of Ekeland's variational principle is derived and applied to establish a sufficient condition for Levitin-Polyak well-posedness of a class of generalized vector quasi-equilibrium problems.
    Mathematics Subject Classification: 90C31, 49J53.

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