Transformation of quasiconvex functions to eliminate local minima
type: Item
instance of: scholarly article
title: Transformation of quasiconvex functions to eliminate local minima
zbMATH Open document ID: 1404.90100
author: Suliman Al-Homidan
author: Nicolas Hadjisavvas
author: Loai Shaalan
published in: Journal of Optimization Theory and Applications
publication date: 2018-06-08T00:00:00Z
review text: It is proved that any lower semicontinuous quasiconvex function \(f\) may be written as a composition of two functions \(f = h~ o~ g\), where \(h\) is nondecreasing and \(g\) is quasiconvex and each of its local minimum is at the same time its global minimum. Therefore, the minimization of any lower semicontinuous quasiconvex function \(f\) can be reduced to the minimization of the function \(g\), whose local and global minima coincide. The authors prove this result by making use of some continuity properties of so-called ``adjusted sublevel sets'' and ``sublevel set operators''. The results of the paper make the minimization of lower semicontinuous quasiconvex functions easier.
reviewed by: Karel Zimmermann
Mathematics Subject Classification ID: 90C26
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 26A51
Mathematics Subject Classification ID: 26B25
zbMATH DE Number: 6882321
zbMATH Keywords: quasiconvex function
zbMATH Keywords: generalized convexity
zbMATH Keywords: adjusted sublevel sets
zbMATH Keywords: normal operator
MaRDI profile type: Publication
full work available at URL: s10957-018-1223-7
OpenAlex ID: W2792721815
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DOI: 10.1007/S10957-018-1223-7
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description: scientific article; zbMATH DE number 6882321