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Error estimates for the approximation of multibang control problems

Author

Listed:
  • Christian Clason

    (University Duisburg-Essen)

  • Thi Bich Tram Do

    (University Duisburg-Essen)

  • Frank Pörner

    (University of Würzburg)

Abstract

This work is concerned with optimal control problems where the objective functional consists of a tracking-type functional and an additional “multibang” regularization functional that promotes optimal control taking values from a given discrete set pointwise almost everywhere. Under a regularity condition on the set where these discrete values are attained, error estimates for the Moreau–Yosida approximation (which allows its solution by a semismooth Newton method) and the discretization of the problem are derived. Numerical results support the theoretical findings.

Suggested Citation

  • Christian Clason & Thi Bich Tram Do & Frank Pörner, 2018. "Error estimates for the approximation of multibang control problems," Computational Optimization and Applications, Springer, vol. 71(3), pages 857-878, December.
    • Handle: RePEc:spr:coopap:v:71:y:2018:i:3:d:10.1007_s10589-018-0026-y
    DOI: 10.1007/s10589-018-0026-y
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    References listed on IDEAS

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    1. Klaus Deckelnick & Michael Hinze, 2012. "A note on the approximation of elliptic control problems with bang-bang controls," Computational Optimization and Applications, Springer, vol. 51(2), pages 931-939, March.
    2. Georg Stadler, 2009. "Elliptic optimal control problems with L 1 -control cost and applications for the placement of control devices," Computational Optimization and Applications, Springer, vol. 44(2), pages 159-181, November.
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