Strict feasibility of pseudomonotone set-valued variational inequalities

Abstract

In this article, we use degree theory developed in Kien et al. [B.T. Kien, M.-M. Wong, N.C. Wong, and J.C. Yao, Degree theory for generalized variational inequalities and applications, Eur. J. Oper. Res. 193 (2009), pp. 12–22.] to prove a result on the existence of solutions to set-valued variational inequality under a weak coercivity condition, provided that the set-valued mapping is upper semicontinuous with nonempty compact convex values. If the set-valued mapping is pseudomonotone in the sense of Karamardian and upper semicontinuous with nonempty compact convex values, it is shown that the set-valued variational inequality is strictly feasible if and only if its solution set is nonempty and bounded.

Keywords:

• set-valued variational inequalities
• pseudomonotone
• strict feasibility

AMS Subject Classifications::

• 90C33
• 47H11
• 54C60

Acknowledgements

The authors are grateful to the referees for valuable suggestions. This work is partially supported by National Natural Science Foundation of China (No. 10701059).