Optimal control problems for the heat equation with pointwise bilateral control-state constraints are considered. A locally superlinearly convergent numerical solution algorithm is proposed and its mesh independence is established. Further, for the efficient numerical solution reduced space and Schur complement based preconditioners are proposed which take into account the active and inactive set structure of the problem. The paper ends by numerical tests illustrating our theoretical findings and comparing the efficiency of the proposed preconditioners.
Mots-clés : bilateral control-state constraints, heat equation, mesh independence, optimal control, PDE-constrained optimization, semismooth Newton method
@article{COCV_2009__15_3_626_0,
author = {Hinterm\"uller, Michael and Kopacka, Ian and Volkwein, Stefan},
title = {Mesh-independence and preconditioning for solving parabolic control problems with mixed control-state constraints},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {626--652},
publisher = {EDP-Sciences},
volume = {15},
number = {3},
year = {2009},
doi = {10.1051/cocv:2008042},
mrnumber = {2542576},
zbl = {1167.49027},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2008042/}
}
TY - JOUR AU - Hintermüller, Michael AU - Kopacka, Ian AU - Volkwein, Stefan TI - Mesh-independence and preconditioning for solving parabolic control problems with mixed control-state constraints JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2009 SP - 626 EP - 652 VL - 15 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2008042/ DO - 10.1051/cocv:2008042 LA - en ID - COCV_2009__15_3_626_0 ER -
%0 Journal Article %A Hintermüller, Michael %A Kopacka, Ian %A Volkwein, Stefan %T Mesh-independence and preconditioning for solving parabolic control problems with mixed control-state constraints %J ESAIM: Control, Optimisation and Calculus of Variations %D 2009 %P 626-652 %V 15 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2008042/ %R 10.1051/cocv:2008042 %G en %F COCV_2009__15_3_626_0
Hintermüller, Michael; Kopacka, Ian; Volkwein, Stefan. Mesh-independence and preconditioning for solving parabolic control problems with mixed control-state constraints. ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 3, pp. 626-652. doi : 10.1051/cocv:2008042. http://www.numdam.org/articles/10.1051/cocv:2008042/
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