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Optimal Control of Obstacle Problems: Existence of LagrangeMultipliers

Published online by Cambridge University Press:  15 August 2002

Maïtine Bergounioux  and
Fulbert Mignot
Maïtine Bergounioux
Affiliation:
Département de Mathématiques, UMR 6628, Université d'Orléans, BP. 6759, 45067 Orléans Cedex 2, France; Maitine.Bergounioux@labomath.univ-orleans.fr.
Fulbert Mignot
Affiliation:
Laboratoire de Mathématique, bâtiment 425, Université Paris-Sud, 91405 Orsay, France; Fulbert.Mignot@math.u-psud.fr.
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Abstract

We study first order optimality systems for the control of a system governed by a variational inequality and deal with Lagrange multipliers: is it possible to associate to each pointwise constraint a multiplier to get a “good” optimality system? We give positive and negative answers for the finite and infinite dimensional cases. These results are compared with the previous ones got by penalization or differentiation.

Keywords

Variational inequalitiesoptimal controlLagrange multiplierobstacle problem.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 5 , 2000 , pp. 45 - 70
Copyright
© EDP Sciences, SMAI, 2000

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