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

Published online by Cambridge University Press:  15 August 2002

Fredi Tröltzsch  and
Stefan Volkwein
Fredi Tröltzsch
Affiliation:
Technische Universität Berlin, Fakultät II – Mathematik und Naturwissenschaften, Sekretariat MA 4-5, Straße des 17 Juni 136, 10623 Berlin, Germany; troeltz@math.tu-berlin.de.
Stefan Volkwein
Affiliation:
Karl–Franzens–Universität Graz, Institut für Mathematik, Heinrichstrasse 36, 8010 Graz, Austria; stefan.volkwein@uni-graz.at.
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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.

Keywords

Burgers' equationSQP methodsgeneralized Newton's methodprimal-dual methodsactive set strategy.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 6 , 2001 , pp. 649 - 674
Copyright
© EDP Sciences, SMAI, 2001

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