# POD a-posteriori error based inexact SQP method for bilinear elliptic optimal control problems

Martin Kahlbacher; Stefan Volkwein

- Volume: 46, Issue: 2, page 491-511
- ISSN: 0764-583X

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topKahlbacher, Martin, and 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 46.2 (2012): 491-511. <http://eudml.org/doc/273212>.

@article{Kahlbacher2012,

abstract = {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.},

author = {Kahlbacher, Martin, Volkwein, Stefan},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {optimal control; inexact SQP method; proper orthogonal decomposition; a-posteriori error estimates; bilinear elliptic equation; inexact sequential quadratic programming method},

language = {eng},

number = {2},

pages = {491-511},

publisher = {EDP-Sciences},

title = {POD a-posteriori error based inexact SQP method for bilinear elliptic optimal control problems},

url = {http://eudml.org/doc/273212},

volume = {46},

year = {2012},

}

TY - JOUR

AU - Kahlbacher, Martin

AU - Volkwein, Stefan

TI - POD a-posteriori error based inexact SQP method for bilinear elliptic optimal control problems

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2012

PB - EDP-Sciences

VL - 46

IS - 2

SP - 491

EP - 511

AB - 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.

LA - eng

KW - optimal control; inexact SQP method; proper orthogonal decomposition; a-posteriori error estimates; bilinear elliptic equation; inexact sequential quadratic programming method

UR - http://eudml.org/doc/273212

ER -

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