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Quantifying Retardation in Simulation Based Optimization

In: Optimization, Simulation, and Control

Author

Listed:
  • Andreas Griewank

    (Humboldt University Berlin)

  • Adel Hamdi

    (Institut National des Sciences Appliques de Rouen)

  • Emre Özkaya

    (RWTH Aachen University)

Abstract

In many applications one wishes to optimize designs on the basis of an established simulation tool. We consider the situation where “simulation” means solving a system of state equations by a fixed point iteration. “Optimization” may then be performed by appending an adjoint solver and an iteration step on the design variables. The main mathematical goal of this chapter is to quantify and estimate the retardation factor, i.e., the complexity of an optimization run compared to that of a single simulation, measured in terms of contraction rates. It is generally believed that the retardation factor should be bounded by a reasonably small number irrespective of discretization widths and other incidental quantities. We show that this is indeed the case for a simple elliptic control problem, when the state equations are solved by Jacobi or a multigrid V-cycle. Moreover, there is strong dependence on a regularization term. This is also shown to be true when the state equation is solved by Newton’s method and the projected Hessian is explicitly available

Suggested Citation

  • Andreas Griewank & Adel Hamdi & Emre Özkaya, 2013. "Quantifying Retardation in Simulation Based Optimization," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Rentsen Enkhbat & E. N. Pistikopoulos (ed.), Optimization, Simulation, and Control, edition 127, pages 79-96, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-5131-0_6
    DOI: 10.1007/978-1-4614-5131-0_6
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