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Estimation of Regularization Parameters in Elliptic Optimal Control Problems by POD Model Reduction

  • Martin Kahlbacher
  • Stefan Volkwein
Part of the IFIP Advances in Information and Communication Technology book series (IFIPAICT, volume 312)

Abstract

In this article parameter estimation problems for a nonlinear elliptic problem are considered. Using Tikhonov regularization techniques the identification problems are formulated in terms of optimal control problems which are solved numerically by an augmented Lagrangian method combined with a globalized sequential quadratic programming algorithm. For the discretization of the partial differential equations a Galerkin scheme based on proper orthogonal decomposition (POD) is utilized, which leads to a fast optimization solver. This method is utilized in a bilevel optimization problem to determine the parameters for the Tikhonov regularization. Numerical examples illustrate the efficiency of the proposed approach.

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Copyright information

© IFIP International Federation for Information Processing 2009

Authors and Affiliations

  • Martin Kahlbacher
    • 1
  • Stefan Volkwein
    • 1
  1. 1.Institute for Mathematics and Scientific ComputingUniversity of GrazGrazAustria

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