Convergence and regularization results for optimal control problems with sparsity functional
Chemnitz University of Technology,
Faculty of Mathematics,
09107 Chemnitz, Germany.
2 Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstrae 69, 4040 Linz, Austria. email@example.com
Revised: 9 February 2010
Revised: 18 May 2010
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.
Mathematics Subject Classification: 49M05 / 65N15 / 65N30 / 49N45
Key words: Non-smooth optimization / sparsity / regularization error estimates / finite elements / discretization error estimates
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