Lipschitz and Hölder global optimization using space-filling curves
type: Item
instance of: scholarly article
title: Lipschitz and Hölder global optimization using space-filling curves
zbMATH Open document ID: 1201.65101
published in: Applied Numerical Mathematics
publication date: 2010-05-06T00:00:00Z
review text: The authors present and analyse four algorithms for the global optimisation of a scalar-valued function satisfying a Lipschitz condition that has \(n\) bound constrained arguments. The connecting idea is the usage of a space-filling Hilbert curve and a transformation of the multi-dimensional formulation to a univariate one. Two algorithms are based on a global approximation of the Hölder constant for the resulting univariate function. The other two algorithms exploit a so-called local tuning. Furthermore, both approaches can be combined with a so-called local improvement resulting in four different methods. The performance of the algorithms are analyzed for numerous test functions and \(n=2,3,4\). The results are presented and discussed in detail.
reviewed by: Andrea Walther
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C26
Mathematics Subject Classification ID: 65Y20
zbMATH DE Number: 5704983
zbMATH Keywords: global optimization
zbMATH Keywords: Lipschitz and Hölder functions
zbMATH Keywords: local information
zbMATH Keywords: space-filling curves approximations
zbMATH Keywords: algorithms
zbMATH Keywords: performance
author: Daniela Lera
author: Yaroslav D. Sergeyev
describes a project that uses: Global Optimization Toolbox For Maple
describes a project that uses: LGO
describes a project that uses: Algorithm 829
MaRDI profile type: Publication
full work available at URL: j.apnum.2009.10.004
OpenAlex ID: W2027985480
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DOI: 10.1016/J.APNUM.2009.10.004
description: scientific article; zbMATH DE number 5704983