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Numerical optimal control of the wave equation: optimal boundary control of a string to rest in finite time

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  • Gerdts, Matthias
  • Greif, Günter
  • Pesch, Hans Josef

Abstract

In many real-life applications of optimal control problems with constraints in form of partial differential equations (PDEs), hyperbolic equations are involved which typically describe transport processes. Since hyperbolic equations usually propagate discontinuities of initial or boundary conditions into the domain on which the solution lives or can develop discontinuities even in the presence of smooth data, problems of this type constitute a severe challenge for both theory and numerics of PDE constrained optimization.

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  • 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.
    • Handle: RePEc:eee:matcom:v:79:y:2008:i:4:p:1020-1032
    DOI: 10.1016/j.matcom.2008.02.014
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    References listed on IDEAS

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    1. M. Gugat, 2002. "Analytic Solutions of L∞ Optimal Control Problems for the Wave Equation," Journal of Optimization Theory and Applications, Springer, vol. 114(2), pages 397-421, August.
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    Cited by:

    1. Pablos, Blanca & Gerdts, Matthias, 2021. "Substructure exploitation of a nonsmooth Newton method for large-scale optimal control problems with full discretization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 641-658.
    2. 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.
    3. Gerasimos G. Rigatos, 2016. "Boundary Control Of The Black–Scholes Pde For Option Dynamics Stabilization," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 1-29, June.

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