Abstract
This paper introduces a new concept of exceptional family of elements for a finite-dimensional generalized variational inequality problem. Based on the topological degree theory of set-valued mappings, an alternative theorem is obtained which says that the generalized variational inequality has either a solution or an exceptional family of elements. As an application, we present a sufficient condition to ensure the existence of a solution to the variational inequality. The set-valued mapping is assumed to be upper semicontinuous with nonempty compact convex values.
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The authors are grateful to the referees for valuable suggestions. This work is partially supported by National Natural Science Foundation of China (No. 10701059) and by Sichuan Youth Science and Technology Foundation (No. 06ZQ026-013).
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Liu, Z., He, Y. Exceptional family of elements for generalized variational inequalities. J Glob Optim 48, 465–471 (2010). https://doi.org/10.1007/s10898-009-9500-5
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DOI: https://doi.org/10.1007/s10898-009-9500-5