Invertibility of functional Galois connections

Marianne Akian; Stéphane Gaubert; Vassili Kolokoltsov

doi:10.1016/S1631-073X(02)02594-3

Invertibility of functional Galois connections
[Inversibilité des correspondances de Galois fonctionnelles]

Marianne Akian ¹ ; Stéphane Gaubert ¹ ; Vassili Kolokoltsov ^2,³

¹ INRIA, Domaine de Voluceau, BP 105, 78153 Le Chesnay cedex, France
² Dep. of Computing and Mathematics, Nottingham Trent University, Burton Street, Nottingham NG1 4BU, UK
³ Institute for Information Transmission Problems of Russian Academy of Science, Moscow, Russia

Comptes Rendus. Mathématique, Volume 335 (2002) no. 11, pp. 883-888.

Résumé
Abstract

On considère des équations de la forme Bf=g, où B est une correspondance de Galois entre des treillis de fonctions, ce qui inclut le cas où B est la transformation de Fenchel, ou plus généralement une conjugaison de Moreau. Nous caractérisons l'existence et l'unicité d'une solution f, en termes de sous-différentiels généralisés, et étendons ainsi le théorème de couverture de K. Zimmermann pour les équations linéaires max-plus.

We consider equations of the form Bf=g, where B is a Galois connection between lattices of functions. This includes the case where B is the Fenchel transform, or more generally a Moreau conjugacy. We characterize the existence and uniqueness of a solution f in terms of generalized subdifferentials, which extends K. Zimmermann's covering theorem for max-plus linear equations.

Reçu le : 2002-06-12
Accepté le : 2002-10-16
Publié le : 2002-11-14

DOI : 10.1016/S1631-073X(02)02594-3

Affiliations des auteurs :

Marianne Akian ¹ ; Stéphane Gaubert ¹ ; Vassili Kolokoltsov ^{2, 3}

¹ INRIA, Domaine de Voluceau, BP 105, 78153 Le Chesnay cedex, France
² Dep. of Computing and Mathematics, Nottingham Trent University, Burton Street, Nottingham NG1 4BU, UK
³ Institute for Information Transmission Problems of Russian Academy of Science, Moscow, Russia

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     author = {Marianne Akian and St\'ephane Gaubert and Vassili Kolokoltsov},
     title = {Invertibility of functional {Galois} connections},
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     pages = {883--888},
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     doi = {10.1016/S1631-073X(02)02594-3},
     language = {en},
}

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Marianne Akian; Stéphane Gaubert; Vassili Kolokoltsov. Invertibility of functional Galois connections. Comptes Rendus. Mathématique, Volume 335 (2002) no. 11, pp. 883-888. doi : 10.1016/S1631-073X(02)02594-3. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02594-3/

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