Inversibilité des correspondances de Galois fonctionnelles

Marianne Akian; Stéphane Gaubert; Vassili Kolokoltsov

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

Inversibilité des correspondances de Galois fonctionnelles

Translated title of the contribution: Invertibility of functional Galois connections

Marianne Akian
, Stéphane Gaubert
, Vassili Kolokoltsov

Research output: Contribution to journal › Article › peer-review

Abstract

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 maxplus linear equations.

Translated title of the contribution	Invertibility of functional Galois connections
Original language	French
Pages (from-to)	883-888
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	335
Issue number	11
DOIs	https://doi.org/10.1016/S1631-073X(02)02594-3
Publication status	Published - 1 Dec 2002

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title = "Inversibilit{\'e} des correspondances de Galois fonctionnelles",

abstract = "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 maxplus linear equations.",

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AU - Akian, Marianne

AU - Gaubert, Stéphane

AU - Kolokoltsov, Vassili

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N2 - 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 maxplus linear equations.

AB - 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 maxplus linear equations.

UR - https://www.scopus.com/pages/publications/0038053075

U2 - 10.1016/S1631-073X(02)02594-3

DO - 10.1016/S1631-073X(02)02594-3

M3 - Article

AN - SCOPUS:0038053075

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SP - 883

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JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 11

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Inversibilité des correspondances de Galois fonctionnelles

Abstract

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