Set coverings and invertibility of Functional Galois Connections

Marianne Akian (1) , Stéphane Gaubert (1) , Vassili Kolokoltsov (2)

1 MAXPLUS - Max-plus algebras and mathematics of decision
2 Institute for Information Transmission Problems

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.

Domaines: Analyse fonctionnelle [math.FA]

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⟩