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

Bouthat, Ludovick; Mashreghi, Javad, & Morneau-Guérin, Frédéric (2025). On the Geometry of the Birkhoff Polytope II. The Schatten p-norms. Acta Scientiarum Mathematicarum, 91 (3-4), 401-419. https://doi.org/10.1007/s44146-024-00153-7

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Item Type:	Journal Articles
Refereed:	Yes
Status:	Published
Abstract:	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.
Official URL:	https://link.springer.com/article/10.1007/s44146-0...
Depositor:	Morneau-Guérin, Frédéric
Owner / Manager:	Frédéric Morneau-Guérin
Deposited:	11 Jul 2024 15:07
Last Modified:	07 Dec 2025 19:16

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