In this paper, the global minimization problem of a multi-dimensional black-box Lipschitzian function is considered. In order to pass from the original Lipschitz multi-dimensional problem to a univariate one, an approach using space-filling curves to reduce the dimension is applied. The method does not use derivatives and, at each iteration, works with a set of estimates of the Hölder constant of the reduced one-dimensional problem. A two-phase technique is applied to accelerate the search of the global minimum. Numerical experiments carried out on several hundreds of test functions show a promising performance of the discussed algorithm in comparison with its direct competitors.

A two-phase approach in a global optimization algorithm using multiple estimates of Hölder constants

Lera D.
Primo
;
2019

Abstract

In this paper, the global minimization problem of a multi-dimensional black-box Lipschitzian function is considered. In order to pass from the original Lipschitz multi-dimensional problem to a univariate one, an approach using space-filling curves to reduce the dimension is applied. The method does not use derivatives and, at each iteration, works with a set of estimates of the Hölder constant of the reduced one-dimensional problem. A two-phase technique is applied to accelerate the search of the global minimum. Numerical experiments carried out on several hundreds of test functions show a promising performance of the discussed algorithm in comparison with its direct competitors.
File in questo prodotto:
File Dimensione Formato  
Proceedings-LEGO.pdf

accesso aperto

Tipologia: versione editoriale
Dimensione 633.26 kB
Formato Adobe PDF
633.26 kB Adobe PDF Visualizza/Apri

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/11584/284511
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? ND
social impact