Abstract
A recent global optimization algorithm using decomposition (GOP), due to Floudas and Visweswaran, when specialized to the case of polynomial functions is shown to be equivalent to an interval arithmetic global optimization algorithm which applies natural extension to the cord-slope form of Taylor's expansion. Several more efficient variants using other forms of interval arithmetic are explored. Extensions to rational functions are presented. Comparative computational experiences are reported.
Résumé
On montre que l'algorithme récent d'optimisation globale basé sur la décomposition du à Floudas et Visweswaran, lorsqu'on le spécialise au cas de fonctions polynômiales, est équivalent à une méthode d'optimisation globale basée sur l'arithmétique d'intervalles, qui applique l'extension naturelle à la forme de la pente de la corde du développement de Taylor. Plusieurs variantes plus efficaces utilisant d'autres formes de l'arithmétique d'intervalles sont explorées. On propose des extensions au cas des fonctions fractionnaires. On présente des résultats de calcul comparatifs.
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Hansen, P., Jaumard, B. & Xiong, J. Decomposition and interval arithmetic applied to global minimization of polynomial and rational functions. J Glob Optim 3, 421–437 (1993). https://doi.org/10.1007/BF01096413
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DOI: https://doi.org/10.1007/BF01096413