Journal article
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 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 \$\backslash\$circ f\$ where \$H: \$\backslash\$dR\^m \$\backslash\$mapsto \$\backslash\$dR\$ is convex and \$f: \$\backslash\$dR\^n \$\backslash\$mapsto \$\backslash\$dR\^m\$ is 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 \$\backslash\$circ f\$.
Language: | English |
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Publisher: | Kluwer Academic Publishers |
Year: | 2004 |
Pages: | 145-156 |
Journal subtitle: | International Multidisciplinary Journal To Promote Optimizational Theory and Applications in Engin |
ISSN: | 15732924 and 13894420 |
Types: | Journal article |
DOI: | 10.1023/B:OPTE.0000033372.34626.49 |