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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

Didier Aussel
Dép. de Mathématique, Université de Perpignan, 52 Av. P. Alduy, 66860 Perpignan, France

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

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