A dynamical-system analysis of the optimum s-gradient algorithm

Abstract : We study the asymptotic behaviour of Forsythe's s-optimum gradient algorithm for the minimization of a quadratic function in R^d using a renormalization that converts the algorithm into iterations applied to a probability measure. Bounds on the performance of the algorithm (rate of convergence) are obtained through optimum design theory and the limiting behaviour of the algorithm for s=2 is investigated into details. Algorithms that switch periodically between s=1 and s=2 are shown to converge much faster than when s is fixed at 2.
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Chapitre d'ouvrage
Luc Pronzato, Anatoly Zhigljavsky. Optimal Design and Related Areas in Optimization and Statistics, Springer Verlag, pp.39-80, 2009, Springer Optimization and its Applications, <10.1007/978-0-387-79936-0_3>
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Contributeur : Luc Pronzato <>
Soumis le : mercredi 4 février 2009 - 12:32:25
Dernière modification le : mercredi 4 février 2009 - 13:46:44
Document(s) archivé(s) le : vendredi 12 octobre 2012 - 10:45:15

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Luc Pronzato, Henry Wynn, Anatoly Zhigljavsky. A dynamical-system analysis of the optimum s-gradient algorithm. Luc Pronzato, Anatoly Zhigljavsky. Optimal Design and Related Areas in Optimization and Statistics, Springer Verlag, pp.39-80, 2009, Springer Optimization and its Applications, <10.1007/978-0-387-79936-0_3>. <hal-00358755>

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