On the Geometry of the Birkhoff Polytope II. The Schatten p-norms [r-libre/3320]

Bouthat, Ludovick; Mashreghi, Javad et Morneau-Guérin, Frédéric (2024). On the Geometry of the Birkhoff Polytope II. The Schatten p-norms. Acta Scientiarum Mathematicarum. https://doi.org/10.1007/s44146-024-00153-7

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Catégorie de document :	Articles de revues
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Étape de publication :	Publié
Résumé :	In the first of this series of two articles, we studied some geometrical aspects of the Birkhoff polytope, the compact convex set of all n x n doubly stochastic matrices, namely the Chebyshev center, and the Chebyshev radius of the Birkhoff polytope associated with metrics induced by the operator norms from ln^p to ln^p for 1 \leq p \leq infinity. In the present paper, we take another look at those very questions, but for a different family of matrix norms, namely the Schatten p-norms, for 1 \leq p < infinity. While studying these properties, the intrinsic connection to the minimal trace, which naturally appears in the assignment problem, is also established.
Adresse de la version officielle :	https://link.springer.com/article/10.1007/s44146-0...
Déposant:	Morneau-Guérin, Frédéric
Responsable :	Frédéric Morneau-Guérin
Dépôt :	11 juill. 2024 15:07
Dernière modification :	18 juill. 2024 15:04

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