Duality and gap function for generalized multivalued ε-vector variational inequality

摘要

In this article, a generalized multivalued ε-vector variational inequality (GMVVI)_ε is introduced. An existence theorem for (GMVVI)_ε is established by means of the KKM theorem. Then, a dual ε-vector variational inequality (DVVI)_ε for (GMVVI)_ε is given, and an equivalence relation between (GMVVI)_ε and (DVVI)_ε is proved. Finally, gap functions are also proposed for these two problems, respectively.