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

Yaroslav D. Sergeyev (), Maria Chiara Nasso () and Daniela Lera ()
Additional contact information
Yaroslav D. Sergeyev: Universitá della Calabria
Maria Chiara Nasso: Universitá della Calabria
Daniela Lera: Universitá di Cagliari

Journal of Global Optimization, 2024, vol. 88, issue 3, No 6, 707-722

Abstract: 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.

Keywords: Deterministic global optimization; Lipschitz and Hölder conditions; Space-filling curves; Black-box functions (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10898-022-01216-1 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jglopt:v:88:y:2024:i:3:d:10.1007_s10898-022-01216-1

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10898

DOI: 10.1007/s10898-022-01216-1

Access Statistics for this article

Journal of Global Optimization is currently edited by Sergiy Butenko

More articles in Journal of Global Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().