A Dynamical-System Analysis of the Optimum s-Gradient Algorithm

L. Pronzato (), H.P. Wynn () and A. Zhigljavsky ()
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L. Pronzato: Les Algorithmes – Bât. Euclide B
H.P. Wynn: London School of Economics and Political Science
A. Zhigljavsky: Cardiff University, School of Mathematics

Chapter 3 in Optimal Design and Related Areas in Optimization and Statistics, 2009, pp 39-80 from Springer

Abstract: Summary We study the asymptotic behaviour of Forsythe's s-optimum gradient algorithm for the minimization of a quadratic function in $${\mathbb R}^d$$ 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.

Keywords: Limit Point; Steep Descent; Global Rate; Support Point; Orthogonality Property (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-0-387-79936-0_3

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DOI: 10.1007/978-0-387-79936-0_3

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