Levitin-Polyak well-posedness of a system of generalized vector variational inequality problems

Abstract

In this paper, we introduce two types of Levitin-Polyak well-posedness for a system of generalized vector variational inequalityproblems. By means of a gap function of the system ofgeneralized vector variational inequality problems, we establish equivalence between the two types of Levitin-Polyak well-posedness of the system of generalized vector variational inequality problems and the correspondingwell-posednesses of the minimization problems. We also present some metric characterizations for the two types of Levitin-Polyak well-posedness of the system of generalized vector variational inequalityproblems. The results in this paper generalize, extend and improve some known results in the literature.