# A sensitivity-based extrapolation technique for the numerical solution of state-constrained optimal control problems

Michael Hintermüller; Irwin Yousept

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 16, Issue: 3, page 503-522
- ISSN: 1292-8119

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topHintermüller, Michael, and Yousept, Irwin. "A sensitivity-based extrapolation technique for the numerical solution of state-constrained optimal control problems." ESAIM: Control, Optimisation and Calculus of Variations 16.3 (2010): 503-522. <http://eudml.org/doc/250740>.

@article{Hintermüller2010,

abstract = {
Sensitivity analysis (with respect to the regularization parameter)
of the solution of a class of regularized state constrained
optimal control problems is performed. The theoretical results are
then used to establish an extrapolation-based numerical scheme for
solving the regularized problem for vanishing regularization
parameter. In this context, the extrapolation technique provides
excellent initializations along the sequence of reducing
regularization parameters. Finally, the favorable numerical
behavior of the new method is demonstrated and a comparison to
classical continuation methods is provided.
},

author = {Hintermüller, Michael, Yousept, Irwin},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Extrapolation; mixed control-state constraints; PDE-constrained optimization;
semismooth Newton algorithm; sensitivity; state constraints; extrapolation; semismooth Newton algorithm},

language = {eng},

month = {7},

number = {3},

pages = {503-522},

publisher = {EDP Sciences},

title = {A sensitivity-based extrapolation technique for the numerical solution of state-constrained optimal control problems},

url = {http://eudml.org/doc/250740},

volume = {16},

year = {2010},

}

TY - JOUR

AU - Hintermüller, Michael

AU - Yousept, Irwin

TI - A sensitivity-based extrapolation technique for the numerical solution of state-constrained optimal control problems

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/7//

PB - EDP Sciences

VL - 16

IS - 3

SP - 503

EP - 522

AB -
Sensitivity analysis (with respect to the regularization parameter)
of the solution of a class of regularized state constrained
optimal control problems is performed. The theoretical results are
then used to establish an extrapolation-based numerical scheme for
solving the regularized problem for vanishing regularization
parameter. In this context, the extrapolation technique provides
excellent initializations along the sequence of reducing
regularization parameters. Finally, the favorable numerical
behavior of the new method is demonstrated and a comparison to
classical continuation methods is provided.

LA - eng

KW - Extrapolation; mixed control-state constraints; PDE-constrained optimization;
semismooth Newton algorithm; sensitivity; state constraints; extrapolation; semismooth Newton algorithm

UR - http://eudml.org/doc/250740

ER -

## References

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- C. Meyer, U. Prüfert and F. Tröltzsch, On two numerical methods for stat e–constrained elliptic control problems. Optim. Method. Softw.22 (2007) 871–899.
- F. Tröltzsch, Regular Lagrange multipliers for control problems with mixed pointwise control-state constraints. SIAM J. Optim.15 (2004/2005) 616–634 (electronic).
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- I. Yousept, Vergleich von Lösungsverfahren zur Behandlung elliptischer Optimalsteuerungsprobleme. Master's thesis, TU-Berlin, Germany (2005).

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