In this paper we study Lavrentiev-type regularization concepts for linear-quadratic parabolic control problems with pointwise state constraints. In the first part, we apply classical Lavrentiev regularization to a problem with distributed control, whereas in the second part, a Lavrentiev-type regularization method based on the adjoint operator is applied to boundary control problems with state constraints in the whole domain. The analysis for both classes of control problems is investigated and numerical tests are conducted. Moreover the method is compared with other numerical techniques.
Mots-clés : optimal control, parabolic equation, pointwise state constraints, boundary control, Lavrentiev-type regularization
@article{COCV_2009__15_2_426_0,
author = {Neitzel, Ira and Tr\"oltzsch, Fredi},
title = {On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {426--453},
publisher = {EDP-Sciences},
volume = {15},
number = {2},
year = {2009},
doi = {10.1051/cocv:2008038},
mrnumber = {2513093},
zbl = {1171.49017},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv:2008038/}
}
TY - JOUR AU - Neitzel, Ira AU - Tröltzsch, Fredi TI - On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2009 SP - 426 EP - 453 VL - 15 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2008038/ DO - 10.1051/cocv:2008038 LA - en ID - COCV_2009__15_2_426_0 ER -
%0 Journal Article %A Neitzel, Ira %A Tröltzsch, Fredi %T On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints %J ESAIM: Control, Optimisation and Calculus of Variations %D 2009 %P 426-453 %V 15 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2008038/ %R 10.1051/cocv:2008038 %G en %F COCV_2009__15_2_426_0
Neitzel, Ira; Tröltzsch, Fredi. On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints. ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 2, pp. 426-453. doi : 10.1051/cocv:2008038. http://archive.numdam.org/articles/10.1051/cocv:2008038/
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