Gap functions for generalized vector equilibrium problems via conjugate duality and applications

Abstract

In this article, gap functions for a generalized vector equilibrium problem (GVEP) with explicit constraints are investigated. Under a concept of supremum/infimum of a set, defined in terms of a closure of the set, three kinds of conjugate dual problems are investigated by considering the different perturbations to GVEP. Then, gap functions for GVEP are established by using the weak and strong duality results. As application, the proposed approach is applied to construct gap functions for a vector optimization problem and a generalized vector variational inequality problem.

Keywords:

• generalized vector equilibrium problems
• conjugate duality
• gap functions
• vector optimization problems
• generalized vector variational inequality problems

AMS Subject Classifications::

• 90C46
• 49N15
• 54C60

Acknowledgements

This research was partially supported by the National Natural Science Foundation of China (grant numbers: 11171362 and 11201509).