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Numerical methods using two different approximations of space-filling curves for black-box global optimization

Author

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  • Yaroslav D. Sergeyev

    (Universitá della Calabria
    Lobachevsky State University)

  • Maria Chiara Nasso

    (Universitá della Calabria)

  • Daniela Lera

    (Universitá di Cagliari)

Abstract

In this paper, multi-dimensional global optimization problems are considered, where the objective function is supposed to be Lipschitz continuous, multiextremal, and without a known analytic expression. Two different approximations of Peano-Hilbert curve applied to reduce the problem to a univariate one satisfying the Hölder condition are discussed. The first of them, piecewise-linear approximation, is broadly used in global optimization and not only whereas the second one, non-univalent approximation, is less known. Multi-dimensional geometric algorithms employing these Peano curve approximations are introduced and their convergence conditions are established. Numerical experiments executed on 800 randomly generated test functions taken from the literature show a promising performance of algorithms employing Peano curve approximations w.r.t. their direct competitors.

Suggested Citation

  • Yaroslav D. Sergeyev & Maria Chiara Nasso & Daniela Lera, 2024. "Numerical methods using two different approximations of space-filling curves for black-box global optimization," Journal of Global Optimization, Springer, vol. 88(3), pages 707-722, March.
    • Handle: RePEc:spr:jglopt:v:88:y:2024:i:3:d:10.1007_s10898-022-01216-1
    DOI: 10.1007/s10898-022-01216-1
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    References listed on IDEAS

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    1. 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.
    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. Lera, Daniela & Posypkin, Mikhail & Sergeyev, Yaroslav D., 2021. "Space-filling curves for numerical approximation and visualization of solutions to systems of nonlinear inequalities with applications in robotics," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    4. Yaroslav D. Sergeyev & Marat S. Mukhametzhanov & Dmitri E. Kvasov & Daniela Lera, 2016. "Derivative-Free Local Tuning and Local Improvement Techniques Embedded in the Univariate Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 186-208, October.
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    Cited by:

    1. Ilias Kotsireas & Panos Pardalos & Julius Žilinskas, 2024. "Preface," Journal of Global Optimization, Springer, vol. 88(3), pages 531-532, March.

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