On the geometry of the Birkhoff polytope I: the operator $$\ell ^p_n$$-norms

Bouthat, Ludovick; Mashreghi, Javad; Morneau-Guérin, Frédéric

doi:10.1007/s44146-024-00152-8

Acta Sci. Math. (Szeged)

2024

DOI: 10.1007/s44146-024-00152-8

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On the geometry of the Birkhoff polytope I: the operator $$\ell ^p_n$$-norms

Ludovick Bouthat,

Javad Mashreghi,

Frédéric Morneau-Guérin

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2024

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The diameter of the Birkhoff polytope

Bouthat,

Mashreghi,

Morneau-Guérin

2024

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The geometry of the compact convex set of all n × n n\times n doubly stochastic matrices, a structure frequently referred to as the Birkhoff polytope, has been an active subject of research as of late. Geometric characteristics such as the Chebyshev center and the Chebyshev radius with respect to the operator norms from ℓ n p {\ell }_{n}^{p} to ℓ n p {\ell }_{n}^{p} and the Schatten p p -norms, both for the range 1 ≤ p ≤ ∞ 1\le p\le \infty , have only recently been studied in depth. In this article, we continue in this vein by determining the diameter of the Birkhoff polytope with respect to the metrics induced by the aforementioned matrix norms.

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The diameter of the Birkhoff polytope

Bouthat,

Mashreghi,

Morneau-Guérin

2024

Special Matrices

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On the geometry of the Birkhoff polytope I: the operator $$\ell ^p_n$$-norms

Cited by 1 publication

References 18 publications

The diameter of the Birkhoff polytope

The diameter of the Birkhoff polytope

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