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In this article, we investigate conditions for nonemptiness and compactness of the sets of solutions of pseudomonotone vector variational inequalities by using the concept of asymptotical cones. We show that a pseudomonotone vector variational inequality has a nonempty and compact solution set provided that it is strictly feasible. We also obtain some necessary conditions for the set of solutions of a pseudomonotone vector variational inequality to be nonempty and compact.
Acknowledgements
The authors would like to express their deep thanks to one anonymous referee for his/her helpful comments and suggestions which led to the improvement of this article. This work was partially supported by the National Natural Science Foundation of China (10826064, 10671135), the Specialized Research Fund for the Doctoral Program of Higher Education (20060610005) and the Youth Science Foundation of Sichuan University (07069).