A minimum effort optimal control problem for the wave equation |
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Authors: | Axel Kröner Karl Kunisch |
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Affiliation: | 1. Johann Radon Institute for Computational and Applied Mathematics, Altenberger Strasse 69, 4040, Linz, Austria 2. Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstr. 36, 8010, Graz, Austria
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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. |
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