Mesh-independence and preconditioning for solving parabolic control problems with mixed control-state constraints

Michael Hintermüller; Ian Kopacka; Stefan Volkwein

ESAIM: Control, Optimisation and Calculus of Variations (2008)

  • Volume: 15, Issue: 3, page 626-652
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Hintermüller, Michael, Kopacka, Ian, and Volkwein, Stefan. "Mesh-independence and preconditioning for solving parabolic control problems with mixed control-state constraints." ESAIM: Control, Optimisation and Calculus of Variations 15.3 (2008): 626-652. <http://eudml.org/doc/90930>.

@article{Hintermüller2008,
abstract = { 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. },
author = {Hintermüller, Michael, Kopacka, Ian, Volkwein, Stefan},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Bilateral control-state constraints; heat equation; mesh independence; optimal control; PDE-constrained optimization; semismooth Newton method; bilateral control-state constraints; mesh independence; semismooth Newton method},
language = {eng},
month = {7},
number = {3},
pages = {626-652},
publisher = {EDP Sciences},
title = {Mesh-independence and preconditioning for solving parabolic control problems with mixed control-state constraints},
url = {http://eudml.org/doc/90930},
volume = {15},
year = {2008},
}

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
DA - 2008/7//
PB - EDP Sciences
VL - 15
IS - 3
SP - 626
EP - 652
AB - 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.
LA - eng
KW - Bilateral control-state constraints; heat equation; mesh independence; optimal control; PDE-constrained optimization; semismooth Newton method; bilateral control-state constraints; mesh independence; semismooth Newton method
UR - http://eudml.org/doc/90930
ER -

References

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