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Set coverings and invertibility of Functional Galois Connections

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 Legendre-Fenchel transform, or more generally a Moreau conjugacy. We characterise the existence and uniqueness of a solution f in terms of generalised subdifferentials. This extends a theorem of Vorobyev and Zimmermann, relating solutions of max-plus linear equations and set coverings. We give various illustrations.
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https://hal.inria.fr/inria-00000966
Contributor : Marianne Akian <>
Submitted on : Friday, January 6, 2006 - 4:18:49 PM
Last modification on : Tuesday, July 14, 2020 - 11:04:05 AM

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Marianne Akian, Stéphane Gaubert, Vassili Kolokoltsov. Set coverings and invertibility of Functional Galois Connections. G.L. Litvinov and V.P. Maslov. Idempotent Mathematics and Mathematical Physics, 377 (377), American Mathematical Society, pp.19-51, 2005, Contemporary Mathematics. ⟨inria-00000966⟩

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