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

Abstract

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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.

How to cite

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Wachsmuth, 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 -

References

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