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Convergence and regularization results for optimal control problems with sparsity functional

Published online by Cambridge University Press:  06 August 2010

Gerd Wachsmuth  and
Daniel Wachsmuth
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. daniel.wachsmuth@ricam.oeaw.ac.at
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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 Newton method. 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.

Keywords

Non-smooth optimizationsparsityregularization error estimatesfinite elementsdiscretization error estimates
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 17 , Issue 3 , July 2011 , pp. 858 - 886
Copyright
© EDP Sciences, SMAI, 2010

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