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

Autor: Yaroslav D. Sergeyev, Maria Chiara Nasso, Daniela Lera
Rok vydání: 2022
Předmět:
Zdroj: Journal of Global Optimization.
ISSN: 1573-2916
0925-5001
DOI: 10.1007/s10898-022-01216-1
Popis: 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.
Databáze: OpenAIRE
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