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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.
@article{COCV_2001__6__649_0,
author = {Tr\"oltzsch, Fredi and Volkwein, Stefan},
title = {The {SQP} method for control constrained optimal control of the {Burgers} equation},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {649--674},
publisher = {EDP-Sciences},
volume = {6},
year = {2001},
mrnumber = {1872392},
zbl = {1001.49035},
language = {en},
url = {http://geodesic.mathdoc.fr/item/COCV_2001__6__649_0/}
}
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 PY - 2001 SP - 649 EP - 674 VL - 6 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/item/COCV_2001__6__649_0/ LA - en ID - COCV_2001__6__649_0 ER -
%0 Journal Article %A Tröltzsch, Fredi %A Volkwein, Stefan %T The SQP method for control constrained optimal control of the Burgers equation %J ESAIM: Control, Optimisation and Calculus of Variations %D 2001 %P 649-674 %V 6 %I EDP-Sciences %U http://geodesic.mathdoc.fr/item/COCV_2001__6__649_0/ %G en %F COCV_2001__6__649_0
Tröltzsch, Fredi; Volkwein, Stefan. The SQP method for control constrained optimal control of the Burgers equation. ESAIM: Control, Optimisation and Calculus of Variations, Tome 6 (2001), pp. 649-674. http://geodesic.mathdoc.fr/item/COCV_2001__6__649_0/