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.
@article{M2AN_2012__46_2_491_0,
author = {Kahlbacher, Martin and Volkwein, Stefan},
title = {POD a-posteriori error based inexact SQP method for bilinear elliptic optimal control problems},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {46},
year = {2012},
pages = {491-511},
doi = {10.1051/m2an/2011061},
zbl = {1272.49059},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2012__46_2_491_0}
}
Kahlbacher, Martin; Volkwein, Stefan. POD a-posteriori error based inexact SQP method for bilinear elliptic optimal control problems. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 46 (2012) pp. 491-511. doi : 10.1051/m2an/2011061. http://gdmltest.u-ga.fr/item/M2AN_2012__46_2_491_0/
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