Set coverings and invertibility of Functional Galois Connections
Functional Analysis
2007-05-23 v2
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.
Keywords
Cite
@article{arxiv.math/0403441,
title = {Set coverings and invertibility of Functional Galois Connections},
author = {Marianne Akian and Stephane Gaubert and Vassili Kolokoltsov},
journal= {arXiv preprint arXiv:math/0403441},
year = {2007}
}
Comments
33 pages, 2 Postscript figures; Acknowledgement added