Quantifying Retardation in Simulation Based Optimization

Andreas Griewank (), Adel Hamdi () and Emre Özkaya ()
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Andreas Griewank: Humboldt University Berlin
Adel Hamdi: Institut National des Sciences Appliques de Rouen
Emre Özkaya: RWTH Aachen University

A chapter in Optimization, Simulation, and Control, 2013, pp 79-96 from Springer

Abstract: 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

Keywords: Retardation Factor; Fixed-point Solver; Step Multiplier; Second-order Sufficiency; Full Step Method (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4614-5131-0_6

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DOI: 10.1007/978-1-4614-5131-0_6

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