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Convergence and regularization resultsfor optimal control problems with sparsity functional

Published online by Cambridge University Press:  06 August 2010

Gerd Wachsmuth
Affiliation:
Chemnitz University of Technology, Faculty of Mathematics, 09107 Chemnitz, Germany.
Daniel Wachsmuth
Affiliation:
Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstrae 69, 4040 Linz, Austria. [email protected]
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Abstract

Optimization problems with convex but non-smooth cost functional subject to an elliptic partial differential equation are considered.The non-smoothness arises from a L1-norm in the objective functional. The problem is regularized to permit the use of the semi-smooth Newtonmethod. Error estimates with respect to the regularization parameter are provided. Moreover, finite element approximations are studied. A-priori as well as a-posteriori error estimates are developed and confirmed by numerical experiments.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2010

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