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Zbl 1082.49009
Han, J.; Huang, Z.H.; Fang, S.C.
Solvability of variational inequality problems. (English)
[J] J. Optimization Theory Appl. 122, No. 3, 501-520 (2004). ISSN 0022-3239; ISSN 1573-2878/e

Summary: 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.

MSC 2000:: *49J40 Variational methods including variational inequalities
47J20 Inequalities involving nonlinear operators
90C33 Complementarity problems

Keywords: variational inequalities; complementarity problems; exceptional family of elements; existence theorems

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