Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Quasimonotone variational inequality
  • stability
  • upper semicontinuity
  • lower semicontinuity
  • quasiconvex programming
  • Mosco convergence

Mathematics Subject Classification

49J40; 49K40, 49J52

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Suggested citation

M. Ait Mansour, D. Aussel. “Quasimonotone Variational Inequalities and Quasiconvex Programming: Qualitative Stability.” Journal of Convex Analysis 15 (2008), No. 3, 459–472. https://doi.org/10.68381/jca15033

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Published by Heldermann Verlag, 2008. Rights now held by Banach Press LLC.