The SQP method for control constrained optimal control of the Burgers equation

Fredi Tröltzsch; Stefan Volkwein

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

  • Volume: 6, page 649-674
  • ISSN: 1292-8119

Abstract

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A Lagrange–Newton–SQP method is analyzed for the optimal control of the Burgers equation. Distributed controls are given, which are restricted by pointwise lower and upper bounds. The convergence of the method is proved in appropriate Banach spaces. This proof is based on a weak second-order sufficient optimality condition and the theory of Newton methods for generalized equations in Banach spaces. For the numerical realization a primal-dual active set strategy is applied. Numerical examples are included.

How to cite

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Tröltzsch, Fredi, and Volkwein, Stefan. "The SQP method for control constrained optimal control of the Burgers equation." ESAIM: Control, Optimisation and Calculus of Variations 6 (2010): 649-674. <http://eudml.org/doc/197340>.

@article{Tröltzsch2010,
abstract = { A Lagrange–Newton–SQP method is analyzed for the optimal control of the Burgers equation. Distributed controls are given, which are restricted by pointwise lower and upper bounds. The convergence of the method is proved in appropriate Banach spaces. This proof is based on a weak second-order sufficient optimality condition and the theory of Newton methods for generalized equations in Banach spaces. For the numerical realization a primal-dual active set strategy is applied. Numerical examples are included. },
author = {Tröltzsch, Fredi, Volkwein, Stefan},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Burgers' equation; SQP methods; generalized Newton's method; primal-dual methods; active set strategy.; Burgers equation; SQP methods; generalized Newton method; active set strategy; optimal control},
language = {eng},
month = {3},
pages = {649-674},
publisher = {EDP Sciences},
title = {The SQP method for control constrained optimal control of the Burgers equation},
url = {http://eudml.org/doc/197340},
volume = {6},
year = {2010},
}

TY - JOUR
AU - Tröltzsch, Fredi
AU - Volkwein, Stefan
TI - The SQP method for control constrained optimal control of the Burgers equation
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 6
SP - 649
EP - 674
AB - A Lagrange–Newton–SQP method is analyzed for the optimal control of the Burgers equation. Distributed controls are given, which are restricted by pointwise lower and upper bounds. The convergence of the method is proved in appropriate Banach spaces. This proof is based on a weak second-order sufficient optimality condition and the theory of Newton methods for generalized equations in Banach spaces. For the numerical realization a primal-dual active set strategy is applied. Numerical examples are included.
LA - eng
KW - Burgers' equation; SQP methods; generalized Newton's method; primal-dual methods; active set strategy.; Burgers equation; SQP methods; generalized Newton method; active set strategy; optimal control
UR - http://eudml.org/doc/197340
ER -

References

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