Convergence of Hybrid Space Mapping Algorithms

The space mapping technique is intended for optimization of engineering models which involve very expensive function evaluations. It may be considered a preprocessing method which often provides a very efficient initial phase of an optimization procedure. However, the ultimate rate of convergence ma...

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Bibliographic Details
Published in:Optimization and engineering 2004-06, Vol.5 (2), p.145-156
Main Authors: Madsen, Kaj, Søndergaard, Jacob
Format: Article
Language:English
Subjects:
Algorithms
Convergence
Mapping
Mathematical models
Optimization
Preprocessing
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Summary:The space mapping technique is intended for optimization of engineering models which involve very expensive function evaluations. It may be considered a preprocessing method which often provides a very efficient initial phase of an optimization procedure. However, the ultimate rate of convergence may be poor, or the method may even fail to converge to a stationary point. We consider a convex combination of the space mapping technique with a classical optimization technique. The function to be optimized has the form H [cir f where H : R super( )m arrow right R is convex and f : R super( )n arrow right R super( )mis smooth. Experience indicates that the combined method maintains the initial efficiency of the space mapping technique. We prove that the global convergence property of the classical technique is also maintained: The combined method provides convergence to the set of stationary points of H [cir f.
ISSN:1389-4420
1573-2924
DOI:10.1023/B:OPTE.0000033372.34626.49