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Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 10
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Articles

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

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Pages 2182-2199 | Received 16 May 2012, Accepted 12 Aug 2012, Published online: 14 Sep 2012
 

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.

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Acknowledgements

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

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