Convergence and regularization results for optimal control problems with sparsity functional
ESAIM: Control, Optimisation and Calculus of Variations, Volume 17 (2011) no. 3, p. 858-886

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.

DOI : https://doi.org/10.1051/cocv/2010027
Classification:  49M05,  65N15,  65N30,  49N45
Keywords: 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},
     publisher = {EDP-Sciences},
     volume = {17},
     number = {3},
     year = {2011},
     pages = {858-886},
     doi = {10.1051/cocv/2010027},
     zbl = {1228.49032},
     mrnumber = {2826983},
     language = {en},
     url = {http://www.numdam.org/item/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://www.numdam.org/item/COCV_2011__17_3_858_0/

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