Issue |
ESAIM: COCV
Volume 4, 1999
|
|
---|---|---|
Page(s) | 595 - 608 | |
DOI | https://doi.org/10.1051/cocv:1999124 | |
Published online | 15 August 2002 |
Optimal Control of Semilinear Parabolic Equations with State-Constraints of Bottleneck Type
1
Département de
Mathématiques, UMR 6628, Université d'Orléans,
BP. 6759, 45067 Orléans Cedex 2, France.
2
Technical University of Chemnitz,
Faculty of Mathematics, 09107 Chemnitz, Germany.
Received:
22
July
1998
Revised:
16
March
1999
Revised:
7
October
1999
We consider optimal distributed and boundary control problems for semilinear parabolic equations, where pointwise constraints on the control and pointwise mixed control-state constraints of bottleneck type are given. Our main result states the existence of regular Lagrange multipliers for the state-constraints. Under natural assumptions, we are able to show the existence of bounded and measurable Lagrange multipliers. The method is based on results from the theory of continuous linear programming problems.
Résumé
Nous étudions des problèmes de contrôle optimal gouvernés par des équations aux dérivés partielles paraboliques semilinéaires. Le contrôle est à la fois distribué et frontière et les contraintes sont ponctuelles sur le contrôle d'une part, et mixtes de type “bottleneck” sur le contrôle et l'état. Sous des hypothèses tout à fait naturelles nous prouvons l'existence de multiplicateurs de Lagrange mesurables et bornés. Nous utilisons pour cela des résultats provenant de la programmation mathématique linéaire, continue.
Mathematics Subject Classification: 49K20 / 90C48 / 90C45
Key words: Parabolic equation / optimal control / pointwise state-constraint / bottleneck problem.
© EDP Sciences, SMAI, 1999
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