In this paper the global optimization problem where the objective function is multiextremal and satisfying the Lipschitz condition over a hyperinterval is considered. An algorithm that uses Peano-type space-filling curves to reduce the original Lipschitz multi-dimensional problem to a univariate one satisfying the Hölder condition is proposed. The algorithm at each iteration applies a new geometric technique working with a number of possible Hölder constants chosen from a set of values varying from zero to infinity showing so that ideas introduced in a popular DIRECT method can be used in the Hölder global optimization, as well. Convergence condition are given. Numerical experiments show quite a promising performance of the new technique.

Space-filling curves and multiple estimates of Hölder constants in derivative-free global optimization

LERA, DANIELA;
2016

Abstract

In this paper the global optimization problem where the objective function is multiextremal and satisfying the Lipschitz condition over a hyperinterval is considered. An algorithm that uses Peano-type space-filling curves to reduce the original Lipschitz multi-dimensional problem to a univariate one satisfying the Hölder condition is proposed. The algorithm at each iteration applies a new geometric technique working with a number of possible Hölder constants chosen from a set of values varying from zero to infinity showing so that ideas introduced in a popular DIRECT method can be used in the Hölder global optimization, as well. Convergence condition are given. Numerical experiments show quite a promising performance of the new technique.
9780735413924
Classes of test functions; Derivative-free global optimization; Deterministic numerical algorithms; DIRECT; Hölder functions; Lipschitz functions; Space-filling curves; Physics and astronomy (all)
File in questo prodotto:
File Dimensione Formato  
Proceedings(ICNAAM)AIP2016.pdf

Solo gestori archivio

Descrizione: Articolo principale
Tipologia: versione editoriale
Dimensione 365.99 kB
Formato Adobe PDF
365.99 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11584/188043
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact