Faces of the polytope of doubly substochastic matrices

Lei Cao; Zhi Chen

doi:10.1016/j.laa.2021.11.012

Faces of the polytope of doubly substochastic matrices

Lei Cao, Zhi Chen

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study the faces of the convex polytope of all n x n doubly substochastic matrices, denoted by w_n. We give the necessary and sufficient conditions of a face being nonempty. We also describe all 1-dimensional faces, 2-dimensional faces, and facets of w_n . Moreover, we explore the relation between the faces of w_nand the faces of Ω_n, the convex polytope of all n x n doubly stochastic matrices.

Original language	American English
Pages (from-to)	59-81
Journal	Linear Algebra and its Applications
Volume	637
DOIs	https://doi.org/10.1016/j.laa.2021.11.012
State	Published - Mar 15 2022

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http://nsuworks.nova.edu/math_facarticles/341

Cite this

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title = "Faces of the polytope of doubly substochastic matrices",

abstract = "We study the faces of the convex polytope of all n x n doubly substochastic matrices, denoted by wn. We give the necessary and sufficient conditions of a face being nonempty. We also describe all 1-dimensional faces, 2-dimensional faces, and facets of wn . Moreover, we explore the relation between the faces of wn and the faces of Ωn, the convex polytope of all n x n doubly stochastic matrices.",

author = "Lei Cao and Zhi Chen",

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AU - Cao, Lei

AU - Chen, Zhi

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N2 - We study the faces of the convex polytope of all n x n doubly substochastic matrices, denoted by wn. We give the necessary and sufficient conditions of a face being nonempty. We also describe all 1-dimensional faces, 2-dimensional faces, and facets of wn . Moreover, we explore the relation between the faces of wn and the faces of Ωn, the convex polytope of all n x n doubly stochastic matrices.

AB - We study the faces of the convex polytope of all n x n doubly substochastic matrices, denoted by wn. We give the necessary and sufficient conditions of a face being nonempty. We also describe all 1-dimensional faces, 2-dimensional faces, and facets of wn . Moreover, we explore the relation between the faces of wn and the faces of Ωn, the convex polytope of all n x n doubly stochastic matrices.

U2 - 10.1016/j.laa.2021.11.012

DO - 10.1016/j.laa.2021.11.012

M3 - Article

SN - 0024-3795

VL - 637

SP - 59

EP - 81

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

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