Journal of Optimization Theory and Applications

, Volume 122, Issue 3, pp 501–520 | Cite as

Solvability of Variational Inequality Problems

  • J. Han
  • Z. H. Huang
  • S. C. Fang


This paper presents the new concept of exceptional family of elements for the variational inequality problem with a continuous function over a general unbounded closed convex set. We establish a characterization theorem that can be used to derive several new existence and compactness conditions on the solution set. Our findings generalize well-known results for various types of variational inequality problems. For a pseudomonotone variational inequality problem, our new existence conditions are both sufficient and necessary.

Variational inequalities complementarity problems exceptional family of elements existence theorems 


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Copyright information

© Springer Science+Business Media, Inc. 2004

Authors and Affiliations

  • J. Han
    • 1
  • Z. H. Huang
    • 1
  • S. C. Fang
    • 2
  1. 1.Institute of Applied MathematicsAcademy of Mathematics and System Sciences, Chinese Academy of SciencesBeijingChina
  2. 2.Walter Clark, Industrial Engineering and Operations ResearchNorth Carolina State UniversityRaleighNorth Carolina

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