Invertibility of functional Galois connections
type: Item
instance of: scholarly article
title: Invertibility of functional Galois connections
zbMATH Open document ID: 1022.06001
DOI: 10.1016/S1631-073X(02)02594-3
author: Marianne Akian
author: Stéphane Gaubert
author: Vassili Kolokoltsov
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2003-05-27T00:00:00Z
review text: A functional Galois connection is a dual Galois connection \(B:{\mathcal F}\to {\mathcal G}\) between a sublattice \({\mathcal F}\) of \(\overline \mathbb{R}^Y\) and a sublattice \({\mathcal G}\) of \(\overline \mathbb{R}^X\), where \(X,Y\) are two sets and \(\overline\mathbb{R} =\mathbb{R}\cup \{\pm\infty\}\). The authors consider the following problem: for given \(g\in{\mathcal G}\) and \(X'\subset X\) find \(f\in {\mathcal F}\) such that \(Bf\leq g\), \(Bf(x)=g(x)\), \(\forall x\in X'\). Theorems 2 and 3 give effective conditions on \(g\) (in terms of generalized subdifferentials) for the solution \(f\) to exist and be unique, and so extend Zimmerman's covering theorem for max-plus linear equations.
Mathematics Subject Classification ID: 06A15
Mathematics Subject Classification ID: 49J52
zbMATH DE Number: 1921081
zbMATH Keywords: lattices of functions
zbMATH Keywords: Moreau conjugacy
zbMATH Keywords: functional Galois connections
zbMATH Keywords: dual Galois connections
zbMATH Keywords: generalized subdifferentials
zbMATH Keywords: covering theorem
zbMATH Keywords: max-plus linear equations
reviewed by: V. N. Saliĭ
MaRDI profile type: Publication
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full work available at URL: s1631-073x(02)02594-3
OpenAlex ID: W2073051433
description: scientific article; zbMATH DE number 1921081