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Chapitre D'ouvrage Année : 2009

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

Résumé

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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Dates et versions

hal-00358755 , version 1 (04-02-2009)

Identifiants

Citer

Luc Pronzato, Henry P. Wynn, Anatoly A. 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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