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One-Dimensional P-Algorithm with Convergence Rate O(n−3+δ) for Smooth Functions

Author

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  • J. Calvin

    (New Jersey Institute of Technology)

  • A. Žilinskas

    (Vytautas Magnus University)

Abstract

Algorithms based on statistical models compete favorably with other global optimization algorithms as shown by extensive testing results. A theoretical inadequacy of previously used statistical models for smooth objective functions was eliminated by the authors who, in a recent paper, have constructed a P-algorithm for a statistical model for smooth functions. In the present paper, a modification of that P-algorithm with an improved convergence rate is described.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:106:y:2000:i:2:d:10.1023_a:1004699313526
    DOI: 10.1023/A:1004699313526
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    References listed on IDEAS

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    1. J. Calvin & A. Žilinskas, 1999. "On the Convergence of the P-Algorithm for One-Dimensional Global Optimization of Smooth Functions," Journal of Optimization Theory and Applications, Springer, vol. 102(3), pages 479-495, September.
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    Citations

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    Cited by:

    1. 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.
    2. Daniela Lera & Yaroslav D. Sergeyev, 2018. "GOSH: derivative-free global optimization using multi-dimensional space-filling curves," Journal of Global Optimization, Springer, vol. 71(1), pages 193-211, May.
    3. Antanas Žilinskas & James Calvin, 2019. "Bi-objective decision making in global optimization based on statistical models," Journal of Global Optimization, Springer, vol. 74(4), pages 599-609, August.
    4. James M. Calvin & Antanas Žilinskas, 2014. "On a Global Optimization Algorithm for Bivariate Smooth Functions," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 528-547, November.
    5. James M. Calvin & Yvonne Chen & Antanas Žilinskas, 2012. "An Adaptive Univariate Global Optimization Algorithm and Its Convergence Rate for Twice Continuously Differentiable Functions," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 628-636, November.

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