Exceptional family of elements for generalized variational inequalities

  • Authors:

  • Zhi Liu;Yiran He

  • Affiliations:

  • Department of Mathematics, Sichuan Normal University, Chengdu, China 610066;Department of Mathematics, Sichuan Normal University, Chengdu, China 610066

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2010

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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.