Set coverings and invertibility of functional Galois connections
By Marianne Akian, Stephane Gaubert, Vassili N. Kolokoltsov. 2004
48 citations recorded by the source corpus.
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.
Subfields: Computational Mechanics, Computational Theory and Mathematics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/080ab7888b5777060809558c0915f9ea3bfd1231
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In Computational Mechanics
In Computational Theory and Mathematics
In Statistical and Nonlinear Physics
Citations in the corpus
- The Maslov dequantization, idempotent and tropical mathematics: A brief introduction (2005, background): “t [17]; see also a finite dimensional version of the separation theorem in [133]. Three papers on this subject by M. Akian, S. Gaubert, V. Kolokoltsov, G. Cohen, J.-P. Quadrat, I. Singer, and C. Walsh [3,5,18] arepublished in this volume. There is an “idempotent” version of the theory of linear repre”
- Minimal half-spaces and external representation of tropical polyhedra (2009, background): “3] (see [1] for a complete recent discussion, including generalizations; see also Corollary 12 and Theorem 15 of [16]), that the apex a− of H belongs to V .”