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.
Mots-clés : non-smooth optimization, sparsity, regularization error estimates, finite elements, discretization error estimates
@article{COCV_2011__17_3_858_0, author = {Wachsmuth, Gerd and Wachsmuth, Daniel}, title = {Convergence and regularization results for optimal control problems with sparsity functional}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {858--886}, publisher = {EDP-Sciences}, volume = {17}, number = {3}, year = {2011}, doi = {10.1051/cocv/2010027}, mrnumber = {2826983}, zbl = {1228.49032}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2010027/} }
TY - JOUR AU - Wachsmuth, Gerd AU - Wachsmuth, Daniel TI - Convergence and regularization results for optimal control problems with sparsity functional JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2011 SP - 858 EP - 886 VL - 17 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2010027/ DO - 10.1051/cocv/2010027 LA - en ID - COCV_2011__17_3_858_0 ER -
%0 Journal Article %A Wachsmuth, Gerd %A Wachsmuth, Daniel %T Convergence and regularization results for optimal control problems with sparsity functional %J ESAIM: Control, Optimisation and Calculus of Variations %D 2011 %P 858-886 %V 17 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2010027/ %R 10.1051/cocv/2010027 %G en %F COCV_2011__17_3_858_0
Wachsmuth, Gerd; Wachsmuth, Daniel. Convergence and regularization results for optimal control problems with sparsity functional. ESAIM: Control, Optimisation and Calculus of Variations, Volume 17 (2011) no. 3, pp. 858-886. doi : 10.1051/cocv/2010027. http://archive.numdam.org/articles/10.1051/cocv/2010027/
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