Journal of Convex Analysis 15 (2008), No. 3, 459--472
Copyright Heldermann Verlag 2008
Quasimonotone Variational Inequalities and Quasiconvex Programming: Qualitative Stability
Mohamed Ait Mansour
Université Cadi Ayyad, Faculté Poly-Disciplinaire, Route Sidi Bouzid, 4600 Safi, Morocco
maitmansour@hotmail.com
Didier Aussel
Dép. de Mathématique, Université de Perpignan, 52 Av. P. Alduy, 66860 Perpignan, France
aussel@univ-perp.fr
We consider quasimonotone Stampacchia variational inequalities subject to perturbations, both on the set-valued operator and on the constraint set. We establish continuity properties, upper semicontinuity and lower semicontinuity, of the (possibly set-valued) solution map. Application to quasiconvex optimization is given throughout the concept of normal operator.
Keywords: Quasimonotone variational inequality, stability, upper semicontinuity, lower semicontinuity, quasiconvex programming, Mosco convergence.
MSC: 49J40; 49K40, 49J52
[ Fulltext-pdf (154 KB)] for subscribers only.