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POD a-posteriori error based inexact SQPmethod for bilinear elliptic optimal control problems∗

Published online by Cambridge University Press:  19 December 2011

Martin Kahlbacher  and
Stefan Volkwein
Martin Kahlbacher
Affiliation:
Universität Graz, Institut für Mathematik und Wissenschaftliches Rechnen, Heinrichstraße 36, 8010 Graz, Austria. martin.kahlbacher@hotmail.com
Stefan Volkwein
Affiliation:
Universität Konstanz, Fachbereich Mathematik und Statistik, Universitätsstraße 10, 78457 Konstanz, Germany; Stefan.Volkwein@uni-konstanz.de

Abstract

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An optimal control problem governed by a bilinear elliptic equation is considered. Thisproblem is solved by the sequential quadratic programming (SQP) method in aninfinite-dimensional framework. In each level of this iterative method the solution oflinear-quadratic subproblem is computed by a Galerkin projection using proper orthogonaldecomposition (POD). Thus, an approximate (inexact) solution of the subproblem isdetermined. Based on a POD a-posteriori error estimator developed byTröltzsch and Volkwein [Comput. Opt. Appl. 44 (2009) 83–115]the difference of the suboptimal to the (unknown) optimal solution of the linear-quadraticsubproblem is estimated. Hence, the inexactness of the discrete solution is controlled insuch a way that locally superlinear or even quadratic rate of convergence of the SQP isensured. Numerical examples illustrate the efficiency for the proposed approach.

Keywords

Optimal controlinexact SQP methodproper orthogonal decompositiona-posteriori error estimatesbilinear elliptic equation

Information

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 2 , March 2012 , pp. 491 - 511
Copyright
© EDP Sciences, SMAI 2011

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