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

Abstract

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.

Keywords:

• generalized multivalued ϵ-vector variational inequalities
• dual ϵ-vector variational inequality
• gap function
• set-valued mapping

AMS Subject Classifications::

• 46A20
• 49J53
• 58E35

Acknowledgements

The authors thank the two anonymous referees for their valuable comments and suggestions, which helped improve this article. This research was partially supported by the National Natural Science Foundation of China (Grant No. 10871216) and the Fundamental Research Funds for the Central Universities (Project No. CDJXS11102212).