Publikation: POD a-posteriori error based inexact SQP method for bilinear elliptic optimal control problems
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2011
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Kahlbacher, Martin
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ESAIM: Mathematical Modelling and Numerical Analysis. 2011, 46(2), pp. 491-511. ISSN 0764-583X. Available under: doi: 10.1051/m2an/2011061
Zusammenfassung
An optimal control problem governed by a bilinear elliptic equation is considered. This problem is solved by the sequential quadratic programming (SQP) method in an infinite-dimensional framework. In each level of this iterative method the solution of linear-quadratic subproblem is computed by a Galerkin projection using proper orthogonal decomposition (POD). Thus, an approximate (inexact) solution of the subproblem is determined. Based on a POD a-posteriori error estimator developed by Tröltzsch and Volkwein [Comput. Opt. Appl. 44 (2009) 83–115] the difference of the suboptimal to the (unknown) optimal solution of the linear-quadratic subproblem is estimated. Hence, the inexactness of the discrete solution is controlled in such a way that locally superlinear or even quadratic rate of convergence of the SQP is ensured. Numerical examples illustrate the efficiency for the proposed approach.
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Fachgebiet (DDC)
510 Mathematik
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Optimal control, inexact SQP method, proper orthogonal decomposition, a-posteriori error estimates, bilinear elliptic equation
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KAHLBACHER, Martin, Stefan VOLKWEIN, 2011. POD a-posteriori error based inexact SQP method for bilinear elliptic optimal control problems. In: ESAIM: Mathematical Modelling and Numerical Analysis. 2011, 46(2), pp. 491-511. ISSN 0764-583X. Available under: doi: 10.1051/m2an/2011061BibTex
@article{Kahlbacher2011apost-18558,
year={2011},
doi={10.1051/m2an/2011061},
title={POD a-posteriori error based inexact SQP method for bilinear elliptic optimal control problems},
number={2},
volume={46},
issn={0764-583X},
journal={ESAIM: Mathematical Modelling and Numerical Analysis},
pages={491--511},
author={Kahlbacher, Martin and Volkwein, Stefan}
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<dcterms:abstract xml:lang="eng">An optimal control problem governed by a bilinear elliptic equation is considered. This problem is solved by the sequential quadratic programming (SQP) method in an infinite-dimensional framework. In each level of this iterative method the solution of linear-quadratic subproblem is computed by a Galerkin projection using proper orthogonal decomposition (POD). Thus, an approximate (inexact) solution of the subproblem is determined. Based on a POD a-posteriori error estimator developed by Tröltzsch and Volkwein [Comput. Opt. Appl. 44 (2009) 83–115] the difference of the suboptimal to the (unknown) optimal solution of the linear-quadratic subproblem is estimated. Hence, the inexactness of the discrete solution is controlled in such a way that locally superlinear or even quadratic rate of convergence of the SQP is ensured. Numerical examples illustrate the efficiency for the proposed approach.</dcterms:abstract>
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