A minimum effort optimal control problem for the wave equation.

Abstract : A minimum effort optimal control problem for the undamped waveequation is considered which involves L∞–control costs. Since the problem isnon-differentiable a regularized problem is introduced. Uniqueness of the solu-tion of the regularized problem is proven and the convergence of the regularizedsolutions is analyzed. Further, a semi-smooth Newton method is formulatedto solve the regularized problems and its superlinear convergence is shown.Thereby special attention has to be paid to the well-posedness of the Newtoniteration. Numerical examples confirm the theoretical results.
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Submitted on : Tuesday, December 16, 2014 - 4:18:04 PM
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Axel Kröner, Karl Kunisch. A minimum effort optimal control problem for the wave equation.. Computational Optimization and Applications, Springer Verlag, 2014, 57 (1), pp.241-270. ⟨hal-01089336v2⟩

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