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Optimality Conditions for Non-Qualified Parabolic Control Problems

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Control and Estimation of Distributed Parameter Systems: Nonlinear Phenomena

Part of the book series: ISNM International Series of Numerical Mathematics ((ISNM,volume 118))

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Abstract

We consider parabolic state constrained optimal control problems where the usual Slater condition is not necessarily satisfied. Instead, a weaker interiority property is assumed. Optimality conditions with a Lagrange multiplier are given. As an application we present an augmented Lagrangian algorithm. Numerical test results are included.

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References

  1. M. Bergounioux, Problèmes de contrôle avec contraintes sur l’état, C. R. Acad. Sci. Paris, Sér. I Math. 310 (1990), 391–396.

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  2. M. Bergounioux, “Optimal control of parabolic problems with state constraints: a penalization method for optimality conditions”, Rapport de Recherche, Université d’Orléans, 1991.

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  4. M. Bergounioux, T. Männikkö, D. Tiba, “On non-qualified parabolic control problems”, Preprint 148, University of Jyväskylä, Department of Mathematics, 1992.

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Author information

Authors and Affiliations

  1. Département de Mathématiques et d’Informatique, U.F.R. Sciences Université d’Orléans, B.P. 6779, F-45067, Orléans Cedex 2, France

    M. Bergounioux

  2. Department of Mathematics, University of Jyväskylä, P.O. Box 35, FIN-40351, Jyväskylä, Finland

    T. Männikkö

  3. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-70700, Bucharest, Romania

    D. Tiba

Authors
  1. M. Bergounioux
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  2. T. Männikkö
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  3. D. Tiba
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Editor information

Editors and Affiliations

  1. Institut für Mathematik, Universitat Graz, Heinrichstrasse 36, A-8010, Graz, Austria

    W. Desch  & F. Kappel  & 

  2. Fachbereich Mathematik, Technische Universitat Berlin, Strasse des 17. Juni 136, D-10623, Berlin, Germany

    K. Kunisch

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© 1994 Springer Basel AG

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Bergounioux, M., Männikkö, T., Tiba, D. (1994). Optimality Conditions for Non-Qualified Parabolic Control Problems. In: Desch, W., Kappel, F., Kunisch, K. (eds) Control and Estimation of Distributed Parameter Systems: Nonlinear Phenomena. ISNM International Series of Numerical Mathematics, vol 118. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8530-0_3

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  • DOI: https://doi.org/10.1007/978-3-0348-8530-0_3

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9666-5

  • Online ISBN: 978-3-0348-8530-0

  • eBook Packages: Springer Book Archive

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