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A minimum effort optimal control problem for the wave equation

Author

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  • Axel Kröner
  • Karl Kunisch

Abstract

A minimum effort optimal control problem for the undamped wave equation is considered which involves L ∞ -control costs. Since the problem is non-differentiable a regularized problem is introduced. Uniqueness of the solution of the regularized problem is proven and the convergence of the regularized solutions is analyzed. Further, a semi-smooth Newton method is formulated to solve the regularized problems and its superlinear convergence is shown. Thereby special attention has to be paid to the well-posedness of the Newton iteration. Numerical examples confirm the theoretical results. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Axel Kröner & Karl Kunisch, 2014. "A minimum effort optimal control problem for the wave equation," Computational Optimization and Applications, Springer, vol. 57(1), pages 241-270, January.
    • Handle: RePEc:spr:coopap:v:57:y:2014:i:1:p:241-270
    DOI: 10.1007/s10589-013-9587-y
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    References listed on IDEAS

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    1. Gerdts, Matthias & Greif, Günter & Pesch, Hans Josef, 2008. "Numerical optimal control of the wave equation: optimal boundary control of a string to rest in finite time," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(4), pages 1020-1032.
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