Levitin-Polyak Well-posedness by Perturbations of a Generalized Vector Mixed Variational Inequality in Banach Spaces
LI Xiao-b · Journal of Sichuan Normal University · 2013
Tykhonov and Levitin-Polyak well-posedness play a central role in the study of optimization problems. Recently,vector optimization problems have been intensively developed. Many researchers have tried to study well-possedness for vector optimization problems. First,the notion of Levitin-Polyak well-posedness by perturbations of a generalized vector mixed variational inequality is introduced in Banach spaces and some metric characterizations for the Levitin-Polyak well-posedness by perturbations of a generalized vector mixed variational inequality are presented. Second,by using the gap function of a generalized vector mixed variational inequality,the equivalent relationship between the Levitin-Polyak well-posedness by perturbations of a generalized vector mixed variational inequality and the related minimizing problem are established. So far,there are no results about Levitin-Polyak well-posedness by perturbations of a generalized vector mixed variational inequality,so it is very interesting to study this problem.