Giannessi, F. and Matroeni, G. and Yang, X. Q.:
A Survey on Vector Variational Inequalities
Bollettino dell'Unione Matematica Italiana Serie 9 2 (2009), fasc. n.1, p. 225-237, (English)
pdf (264 Kb), djvu (128 Kb). | MR 2493652 | Zbl 1170.49007
Sunto
The paper consists in a brief overview on Vector Variational Inequalities (VVI). The connections between VVI and Vector Optimization Problems (VOP) are considered. This leads to point out that necessary optimality conditions for a VOP can be formulated by means of a VVI when the objective function is Gâteaux differentiable and the feasible set is convex. In particular, the existence of solutions and gap functions associated with VVI are analysed. Gap functions provide an equivalent formulation of a VVI, in terms of a constrained extremum problem. Finally, Vector Complementarity Problems and their relationships with VVI are considered.
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