Article

Journal of Optimization Theory and Applications

, Volume 122, Issue 3, pp 501-520

First online:

Solvability of Variational Inequality Problems

  • J. HanAffiliated withInstitute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences
  • , Z. H. HuangAffiliated withInstitute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences
  • , S. C. FangAffiliated withWalter Clark, Industrial Engineering and Operations Research, North Carolina State University

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract

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