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.
@article{BUMI_2009_9_2_1_225_0,
author = {F. Giannessi and G. Matroeni and X. Q. Yang},
title = {A Survey on Vector Variational Inequalities},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {2},
year = {2009},
pages = {225-237},
zbl = {1170.49007},
mrnumber = {2493652},
language = {en},
url = {http://dml.mathdoc.fr/item/BUMI_2009_9_2_1_225_0}
}
Giannessi, F.; Matroeni, G.; Yang, X. Q. A Survey on Vector Variational Inequalities. Bollettino dell'Unione Matematica Italiana, Tome 2 (2009) pp. 225-237. http://gdmltest.u-ga.fr/item/BUMI_2009_9_2_1_225_0/
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