Solvability of Variational Inequality Problems
- Cite this article as:
- Han, J., Huang, Z.H. & Fang, S.C. Journal of Optimization Theory and Applications (2004) 122: 501. doi:10.1023/B:JOTA.0000042593.74934.b7
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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.