Convergence and regularization results for optimal control problems with sparsity functional

Wachsmuth, Gerd; Wachsmuth, Daniel

ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 3, pp. 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.

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