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

Author

Listed:
  • 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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