The diameter of the Birkhoff polytope

The geometry of the compact convex set of all 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...

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Published inSpecial matrices Vol. 12; no. 1; pp. 635 - 655
Main Authors Bouthat, Ludovick, Mashreghi, Javad, Morneau-Guérin, Frédéric
Format Journal Article
LanguageEnglish
Published De Gruyter 24.02.2024
Subjects
15B51
46B20
47B10
52B12
Birkhoff polytope
diameter
Doubly stochastic matrices
norms
operator norm
Schatten
schatten p-norms
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ISSN2300-7451
2300-7451
DOI10.1515/spma-2023-0113

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Abstract The geometry of the compact convex set of all 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 to and the Schatten -norms, both for the range , 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.
AbstractList The geometry of the compact convex set of all n×nn\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 ℓnp{\ell }_{n}^{p} to ℓnp{\ell }_{n}^{p} and the Schatten pp-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.
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.
The geometry of the compact convex set of all 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 to and the Schatten -norms, both for the range , 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.
Author Morneau-Guérin, Frédéric
Bouthat, Ludovick
Mashreghi, Javad
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Snippet The geometry of the compact convex set of all doubly stochastic matrices, a structure frequently referred to as the Birkhoff polytope, has been an active...
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...
The geometry of the compact convex set of all n×nn\times n doubly stochastic matrices, a structure frequently referred to as the Birkhoff polytope, has been an...
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SubjectTerms 15B51
46B20
47B10
52B12
Birkhoff polytope
diameter
Doubly stochastic matrices
norms
operator norm
Schatten
schatten p-norms
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Title The diameter of the Birkhoff polytope
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