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One-Shot Approaches to Design Optimzation

  • Torsten Bosse
  • Nicolas R. Gauger
  • Andreas GriewankEmail author
  • Stefanie Günther
  • Volker Schulz
Chapter
Part of the International Series of Numerical Mathematics book series (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.

Keywords

Simulation Optimization PDE Automatic differentiation Fixed-point solver Retardation factor Convergence Numerics 

Mathematics Subject Classification (2010)

Primary: 90C30 68U20 Secondary: 35Q68 35Q90 35Q93 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Torsten Bosse
    • 2
  • Nicolas R. Gauger
    • 1
  • Andreas Griewank
    • 2
    Email author
  • Stefanie Günther
    • 1
  • Volker Schulz
    • 3
  1. 1.Department of Mathematics and Center for Computational Engineering ScienceRWTH Aachen UniversityAachenGermany
  2. 2.Department of MathematicsHumboldt-Universität zu BerlinBerlinGermany
  3. 3.Universität TrierTrierGermany

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