A minimum effort optimal control problem for the wave equation

Axel Kröner () and Karl Kunisch ()

Computational Optimization and Applications, 2014, vol. 57, issue 1, 270 pages

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

Keywords: Optimal control; Wave equation; Semi-smooth Newton methods; Finite elements (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10589-013-9587-y

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