Comptes Rendus
no. 11
Invertibility of functional Galois connections
[Inversibilité des correspondances de Galois fonctionnelles]
Marianne Akian1 ; Stéphane Gaubert1 ; Vassili Kolokoltsov2, 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.

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