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

In: Optimal Design and Related Areas in Optimization and Statistics

Author

Listed:
  • L. Pronzato

    (Les Algorithmes – Bât. Euclide B)

  • H.P. Wynn

    (London School of Economics and Political Science)

  • A. Zhigljavsky

    (Cardiff University, School of Mathematics)

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.

Suggested Citation

  • L. Pronzato & H.P. Wynn & A. Zhigljavsky, 2009. "A Dynamical-System Analysis of the Optimum s-Gradient Algorithm," Springer Optimization and Its Applications, in: Luc Pronzato & Anatoly Zhigljavsky (ed.), Optimal Design and Related Areas in Optimization and Statistics, chapter 3, pages 39-80, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-79936-0_3
    DOI: 10.1007/978-0-387-79936-0_3
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    Cited by:

    1. Luc Pronzato & Anatoly Zhigljavsky, 2011. "Gradient algorithms for quadratic optimization with fast convergence rates," Computational Optimization and Applications, Springer, vol. 50(3), pages 597-617, December.

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