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On convergence rate of a rectangular partition based global optimization algorithm

Author

Listed:
  • James Calvin

    (New Jersey Institute of Technology)

  • Gražina Gimbutienė

    (Vilnius University)

  • William O. Phillips

    (New Jersey Institute of Technology)

  • Antanas Žilinskas

    (Vilnius University)

Abstract

The convergence rate of a rectangular partition based algorithm is considered. A hyper-rectangle for the subdivision is selected at each step according to a criterion rooted in the statistical models based theory of global optimization; only the objective function values are used to compute the criterion of selection. The convergence rate is analyzed assuming that the objective functions are twice- continuously differentiable and defined on the unit cube in d-dimensional Euclidean space. An asymptotic bound on the convergence rate is established. The results of numerical experiments are included.

Suggested Citation

  • James Calvin & Gražina Gimbutienė & William O. Phillips & Antanas Žilinskas, 2018. "On convergence rate of a rectangular partition based global optimization algorithm," Journal of Global Optimization, Springer, vol. 71(1), pages 165-191, May.
    • Handle: RePEc:spr:jglopt:v:71:y:2018:i:1:d:10.1007_s10898-018-0636-z
    DOI: 10.1007/s10898-018-0636-z
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    References listed on IDEAS

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    1. Anatoly Zhigljavsky & Antanas Žilinskas, 2008. "Stochastic Global Optimization," Springer Optimization and Its Applications, Springer, number 978-0-387-74740-8, June.
    2. J. Calvin & A. Žilinskas, 2000. "One-Dimensional P-Algorithm with Convergence Rate O(n−3+δ) for Smooth Functions," Journal of Optimization Theory and Applications, Springer, vol. 106(2), pages 297-307, August.
    3. Haitao Liu & Shengli Xu & Ying Ma & Xiaofang Wang, 2015. "Global optimization of expensive black box functions using potential Lipschitz constants and response surfaces," Journal of Global Optimization, Springer, vol. 63(2), pages 229-251, October.
    4. Remigijus Paulavičius & Yaroslav Sergeyev & Dmitri Kvasov & Julius Žilinskas, 2014. "Globally-biased Disimpl algorithm for expensive global optimization," Journal of Global Optimization, Springer, vol. 59(2), pages 545-567, July.
    5. Antanas Žilinskas & Julius Žilinskas, 2013. "A hybrid global optimization algorithm for non-linear least squares regression," Journal of Global Optimization, Springer, vol. 56(2), pages 265-277, June.
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    Cited by:

    1. C. J. Price & M. Reale & B. L. Robertson, 2021. "Oscars-ii: an algorithm for bound constrained global optimization," Journal of Global Optimization, Springer, vol. 79(1), pages 39-57, January.
    2. Cuicui Zheng & James Calvin & Craig Gotsman, 2021. "A DIRECT-type global optimization algorithm for image registration," Journal of Global Optimization, Springer, vol. 79(2), pages 431-445, February.
    3. Renato Leone & Yaroslav D. Sergeyev & Anatoly Zhigljavsky, 2018. "Guest editors’ preface to the special issue devoted to the 2nd International Conference “Numerical Computations: Theory and Algorithms”, June 19–25, 2016, Pizzo Calabro, Italy," Journal of Global Optimization, Springer, vol. 71(1), pages 1-4, May.

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