# 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/221893>.

@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; non-smooth optimization},

language = {eng},

month = {8},

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/221893},

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

DA - 2011/8//

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; non-smooth optimization

UR - http://eudml.org/doc/221893

ER -

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