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Tikhonov regularization of control-constrained optimal control problems

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  • Nikolaus Daniels

    (Universität Hamburg)

Abstract

We consider Tikhonov regularization of control-constrained optimal control problems. We present new a-priori estimates for the regularization error assuming measure and source-measure conditions. In the special case of bang–bang solutions, we introduce another assumption to obtain the same convergence rates. This new condition turns out to be useful in the derivation of error estimates for the discretized problem. The necessity of the just mentioned assumptions to obtain certain convergence rates is analyzed. Finally, a numerical example confirms the analytical findings.

Suggested Citation

  • Nikolaus Daniels, 2018. "Tikhonov regularization of control-constrained optimal control problems," Computational Optimization and Applications, Springer, vol. 70(1), pages 295-320, May.
    • Handle: RePEc:spr:coopap:v:70:y:2018:i:1:d:10.1007_s10589-017-9976-8
    DOI: 10.1007/s10589-017-9976-8
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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. Martin Seydenschwanz, 2015. "Convergence results for the discrete regularization of linear-quadratic control problems with bang–bang solutions," Computational Optimization and Applications, Springer, vol. 61(3), pages 731-760, July.
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    Cited by:

    1. Lam Quoc Anh & Tran Quoc Duy & Le Dung Muu & Truong Van Tri, 2021. "The Tikhonov regularization for vector equilibrium problems," Computational Optimization and Applications, Springer, vol. 78(3), pages 769-792, April.

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