# 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 (2009)

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

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topHintermüller, 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 (2009): 626-652. <http://eudml.org/doc/245612>.

@article{Hintermüller2009,

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},

language = {eng},

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/245612},

volume = {15},

year = {2009},

}

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

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

UR - http://eudml.org/doc/245612

ER -

## References

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