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On the Convergence of the P-Algorithm for One-Dimensional Global Optimization of Smooth Functions

Author

Listed:
  • J. Calvin

    (New Jersey Institute of Technology)

  • A. Žilinskas

    (Institute of Mathematics and Informatics)

Abstract

The Wiener process is a widely used statistical model for stochastic global optimization. One of the first optimization algorithms based on a statistical model, the so-called P-algorithm, was based on the Wiener process. Despite many advantages, this process does not give a realistic model for many optimization problems, particularly from the point of view of local behavior. In the present paper, a version of the P-algorithm is constructed based on a stochastic process with smooth sampling functions. It is shown that, in such a case, the algorithm has a better convergence rate than in the case of the Wiener process. A similar convergence rate is proved for a combination of the Wiener model-based P-algorithm with quadratic fit-based local search.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:102:y:1999:i:3:d:10.1023_a:1022677121193
    DOI: 10.1023/A:1022677121193
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    Cited by:

    1. Srivastava, Vaibhav & Bullo, Francesco, 2014. "Knapsack problems with sigmoid utilities: Approximation algorithms via hybrid optimization," European Journal of Operational Research, Elsevier, vol. 236(2), pages 488-498.
    2. R. Cavoretto & A. Rossi & M. S. Mukhametzhanov & Ya. D. Sergeyev, 2021. "On the search of the shape parameter in radial basis functions using univariate global optimization methods," Journal of Global Optimization, Springer, vol. 79(2), pages 305-327, February.
    3. 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.
    4. Logan Mathesen & Giulia Pedrielli & Szu Hui Ng & Zelda B. Zabinsky, 2021. "Stochastic optimization with adaptive restart: a framework for integrated local and global learning," Journal of Global Optimization, Springer, vol. 79(1), pages 87-110, January.

    More about this item

    Keywords

    Global optimization; Gaussian processes;

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