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Studying Convergence of Gradient Algorithms Via Optimal Experimental Design Theory

In: Optimal Design and Related Areas in Optimization and Statistics

Author

Listed:
  • R. Haycroft

    (Cardiff University, School of Mathematics)

  • L. Pronzato

    (Laboratoire I3S, CNRS - UNSA, Les Algorithmes – Bˆat. Euclide B)

  • H. P. Wynn

    (London School of Economics and Political Science)

  • A. Zhigljavsky

    (Cardiff University,School of Mathematics)

Abstract

Summary We study the family of gradient algorithms for solving quadratic optimization problems, where the step-length γ k is chosen according to a particular procedure. To carry out the study, we re-write the algorithms in a normalized form and make a connection with the theory of optimum experimental design. We provide the results of a numerical study which shows that some of the proposed algorithms are extremely efficient.

Suggested Citation

  • R. Haycroft & L. Pronzato & H. P. Wynn & A. Zhigljavsky, 2009. "Studying Convergence of Gradient Algorithms Via Optimal Experimental Design Theory," Springer Optimization and Its Applications, in: Luc Pronzato & Anatoly Zhigljavsky (ed.), Optimal Design and Related Areas in Optimization and Statistics, chapter 2, pages 13-37, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-79936-0_2
    DOI: 10.1007/978-0-387-79936-0_2
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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.
    2. Antanas Žilinskas & Jonathan Gillard & Megan Scammell & Anatoly Zhigljavsky, 2021. "Multistart with early termination of descents," Journal of Global Optimization, Springer, vol. 79(2), pages 447-462, February.

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