Levitin-Polyak Well-Posedness Of Vector Equilibrium Problems

In this thesis, the definitions of Levitin-Polyak well-posedness are extended to vector equilibrium problems and two classes of generalized vector quasi-equilibrium problems。At first,two types of Levitin-Polyak well-posedness of vector equilibrium problems with variable domination structures are introduced. Then, some classical criteria and characterizations for the Levitin-Polyak well-posedness of vector equilibrium problems are shown. Finally, by virtue of a gap function for the vector equilibrium problems, the equivalent relations between the Levitin-Polyak well-posedness for an optimization problem and the Levitin-Polyak well-posedness for the vector equilibrium problems are obtained.At the same time, the definitions of Levitin-Polyak well-posedness for two classes of generalized vector quasi-equilibrium problems are introduced. Then, some classical criteria and characterizations of the Levitin-Polyak well-posedness are investigated. And 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 the 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.