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

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2010

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Kahlbacher, Martin

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Zusammenfassung

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, where in each level of the iterative method the solution of a linear-quadratic subproblem is computed. For numerical realization this subproblem is discretized by a Galerkin projection using proper orthogonal decomposition (POD). Thus, an approximate (inexact) solution of the subproblem is computed. Based on a POD a-posteriori error estimator developed by Tr¨oltzsch and Volkwein (Comput. Optim. Appl., 44:83-115, 2009) the difference of the suboptimal to the (unknown) optimal solution of the linear-quadratic subproblem is estimated. Hence, the inexctness 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.

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510 Mathematik

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ISO 690KAHLBACHER, Martin, Stefan VOLKWEIN, 2010. POD a-posteriori error based inexact SQP method for bilinear elliptic optimal control problems. In: SFB-Report
BibTex
@misc{Kahlbacher2010apost-12776,
  year={2010},
  title={POD a-posteriori error based inexact SQP method for bilinear elliptic optimal control problems},
  author={Kahlbacher, Martin and Volkwein, Stefan}
}
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