A minimum effort optimal control problem for the wave equation

Authors:
Axel Kröner;Karl Kunisch
Affiliations:
Johann Radon Institute for Computational and Applied Mathematics, Linz, Austria 4040;Institute for Mathematics and Scientific Computing, University of Graz, Graz, Austria 8010
Venue:
Computational Optimization and Applications
Year:
2014

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Abstract

A minimum effort optimal control problem for the undamped wave equation is considered which involves L 驴-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.