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One-Shot Approaches to Design Optimzation

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Trends in PDE Constrained Optimization

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 165))

Abstract

The paper describes general methodologies for the solution of design optimization problems. In particular we outline the close relations between a fixed point solver based piggy back approach and a Reduced SQP method in Jacobi and Seidel variants. The convergence rate and general efficacy is shown to be strongly dependent on the characteristics of the state equation and the objective function. In the QP scenario where the state equation is linear and the objective quadratic, finite termination in two steps is obtained by the Seidel variant with Newton state solver and perfect design space preconditioning. More generally, it is shown that the retardation factor between simulation and optimization is bounded below by 2 with the difference depending on a cross-term representing the total sensitivity of the adjoint equation with respect to the design.

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Authors and Affiliations

  1. Department of Mathematics and Center for Computational Engineering Science, RWTH Aachen University, Schinkelstraße 2, 52062, Aachen, Germany

    Nicolas R. Gauger & Stefanie Günther

  2. Department of Mathematics, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    Torsten Bosse & Andreas Griewank

  3. Universität Trier, Universitätsring 15, 54286, Trier, Germany

    Volker Schulz

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  2. Nicolas R. Gauger
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Correspondence to Andreas Griewank .

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Editors and Affiliations

  1. Department Mathematik, Universität Erlangen-Nürnberg, Erlangen, Germany

    Günter Leugering

  2. Institut für Dynamik komplexer technisch, Max-Planck-Institut, Magdeburg, Germany

    Peter Benner

  3. Fakultät Bio- und Chemieingenieurwesen, Technische Universität Dortmund, Dortmund, Germany

    Sebastian Engell

  4. Institut für Mathematik, Humboldt-Universität zu Berlin, Berlin, Germany

    Andreas Griewank

  5. Mathematisches Institut, Universität Basel, Basel, Switzerland

    Helmut Harbrecht

  6. Fachbereich Mathematik Optimierung und Approximation, Universität Hamburg, Hamburg, Germany

    Michael Hinze

  7. Institut für Angewandte Mathematik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany

    Rolf Rannacher

  8. Fachbereich Mathematik, Technische Universität Darmstadt, Darmstadt, Germany

    Stefan Ulbrich

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Bosse, T., Gauger, N.R., Griewank, A., Günther, S., Schulz, V. (2014). One-Shot Approaches to Design Optimzation. In: Leugering, G., et al. Trends in PDE Constrained Optimization. International Series of Numerical Mathematics, vol 165. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-05083-6_5

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