The Fréchet Contingency Array Problem is Max-Plus Linear
Résumé
In this paper we show that the so-called array Fréchet problem in Probability/Statistics is (max, +)-linear. The upper bound of Fréchet is obtained using simple arguments from residuation theory and lattice distributivity. The lower bound is obtained as a loop invariant of a greedy algorithm. The algorithm is based on the max-plus linearity of the Fréchet problem and the Monge property of bivariate distribution.
Domaines
Optimisation et contrôle [math.OC]
Origine : Fichiers produits par l'(les) auteur(s)
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