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Reduced order solution of structured linear systems arising in certain PDE-constrained optimization problems

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  • V. Simoncini

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    Abstract

    The solution of PDE-constrained optimal control problems is a computationally challenging task, and it involves the solution of structured algebraic linear systems whose blocks stem from the discretized first-order optimality conditions. In this paper we analyze the numerical solution of this large-scale system: we first perform a natural order reduction, and then we solve the reduced system iteratively by exploiting specifically designed preconditioning techniques. The analysis is accompanied by numerical experiments on two application problems. Copyright Springer Science+Business Media, LLC 2012

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    File URL: http://hdl.handle.net/10.1007/s10589-012-9464-0
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    Bibliographic Info

    Article provided by Springer in its journal Computational Optimization and Applications.

    Volume (Year): 53 (2012)
    Issue (Month): 2 (October)
    Pages: 591-617

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    Handle: RePEc:spr:coopap:v:53:y:2012:i:2:p:591-617

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    Web page: http://www.springer.com/math/journal/10589

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    Related research

    Keywords: Structured linear systems; Iterative methods; PDE-constraints; Optimization; Preconditioning;

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    1. Luca Bergamaschi & Jacek Gondzio & Manolo Venturin & Giovanni Zilli, 2007. "Inexact constraint preconditioners for linear systems arising in interior point methods," Computational Optimization and Applications, Springer, vol. 36(2), pages 137-147, April.
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