# Convergence and regularization results for optimal control problems with sparsity functional

Gerd Wachsmuth; Daniel Wachsmuth

ESAIM: Control, Optimisation and Calculus of Variations (2011)

- Volume: 17, Issue: 3, page 858-886
- ISSN: 1292-8119

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topWachsmuth, Gerd, and Wachsmuth, Daniel. "Convergence and regularization results for optimal control problems with sparsity functional." ESAIM: Control, Optimisation and Calculus of Variations 17.3 (2011): 858-886. <http://eudml.org/doc/272916>.

@article{Wachsmuth2011,

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.},

author = {Wachsmuth, Gerd, Wachsmuth, Daniel},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {non-smooth optimization; sparsity; regularization error estimates; finite elements; discretization error estimates},

language = {eng},

number = {3},

pages = {858-886},

publisher = {EDP-Sciences},

title = {Convergence and regularization results for optimal control problems with sparsity functional},

url = {http://eudml.org/doc/272916},

volume = {17},

year = {2011},

}

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

PB - EDP-Sciences

VL - 17

IS - 3

SP - 858

EP - 886

AB - 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.

LA - eng

KW - non-smooth optimization; sparsity; regularization error estimates; finite elements; discretization error estimates

UR - http://eudml.org/doc/272916

ER -

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