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, Volume 46 (2012) no. 2, p. 491-511

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.

DOI : https://doi.org/10.1051/m2an/2011061
Classification:  35J47,  49K20,  49M15,  90C20
Keywords: optimal control, inexact SQP method, proper orthogonal decomposition, a-posteriori error estimates, bilinear elliptic equation
@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},
     publisher = {EDP-Sciences},
     volume = {46},
     number = {2},
     year = {2012},
     pages = {491-511},
     doi = {10.1051/m2an/2011061},
     zbl = {1272.49059},
     language = {en},
     url = {http://www.numdam.org/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, Volume 46 (2012) no. 2, pp. 491-511. doi : 10.1051/m2an/2011061. http://www.numdam.org/item/M2AN_2012__46_2_491_0/

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