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A note on the approximation of elliptic control problems with bang-bang controls

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Abstract

In the present work we use the variational approach in order to discretize elliptic optimal control problems with bang-bang controls. We prove error estimates for the resulting scheme and present a numerical example which supports our analytical findings.

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References

  1. Arnautu, V., Langmach, H., Sprekels, J., Tiba, D.: On the approximation and the optimization of plates. Numer. Funct. Anal. Optim. 21, 337–354 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ciarlet, P.G.: The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978)

    MATH  Google Scholar 

  3. Felgenhauer, U.: On stability of bang-bang type controls. SIAM J. Control Optim. 41, 2003 (1843–1867)

    MathSciNet  Google Scholar 

  4. Hinze, M.: A variational discretization concept in control constrained optimization: the linear-quadratic case. Comput. Optim. Appl. 30, 45–61 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Hinze, M., Pinnau, R., Ulbrich, M., Ulbrich, S.: Optimization with PDE Constraints, Mathematical Modelling: Theory and Applications, vol. 23. Springer, Berlin (2009)

    Book  MATH  Google Scholar 

  6. Maurer, H., Mittelmann, H.D.: Optimization techniques for solving elliptic control problems with control and state constraints. Part 1: Boundary control. Comput. Optim. Appl. 16, 29–55 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  7. Maurer, H., Mittelmann, H.D.: Optimization techniques for solving elliptic control problems with control and state constraints. Part 2: Distributed control. Comput. Optim. Appl. 18, 141–160 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  8. Tröltzsch, F.: Optimale Steuerung mit partiellen Differentialgleichungen. Vieweg, Wiesbaden (2005)

    Google Scholar 

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Authors and Affiliations

  1. Institut für Analysis und Numerik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Klaus Deckelnick

  2. Schwerpunkt Optimierung und Approximation, Universität Hamburg, Bundesstraße 55, 20146, Hamburg, Germany

    Michael Hinze

Authors
  1. Klaus Deckelnick
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  2. Michael Hinze
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Correspondence to Michael Hinze.

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Deckelnick, K., Hinze, M. A note on the approximation of elliptic control problems with bang-bang controls. Comput Optim Appl 51, 931–939 (2012). https://doi.org/10.1007/s10589-010-9365-z

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  • DOI: https://doi.org/10.1007/s10589-010-9365-z

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