Article
Enumerating Extreme Points of the Polytopes of Stochastic Tensors: An Optimization Approach
Optimization
Document Type
Article
Publication Date
4-1-2020
Keywords
- Birkhoff polytope,
- Birkhoff-von Neumann theorem,
- Extreme point,
- Line-stochastic tensor,
- Plane-stochastic tensor,
- Polytope,
- Tensor,
- Vertex
Disciplines
Abstract
This paper is concerned with the extreme points of the polytopes of stochastic tensors. By a tensor we mean a multi-dimensional array over the real number field. A line-stochastic tensor is a nonnegative tensor in which the sum of all entries on each line (i.e. one free index) is equal to 1; a plane-stochastic tensor is a nonnegative tensor in which the sum of all entries on each plane (i.e. two free indices) is equal to 1. In enumerating extreme points of the polytopes of line- and plane-stochastic tensors of order 3 and dimension n, we consider the approach by linear optimization and present new lower and upper bounds. We also study the coefficient matrices that define the polytopes.
Additional Comments
National Natural Science Foundatio nof China grant #s: 11571220, 11531001, 11271256; NSFC-ISF research program #: 11561141001; Montenegrin-Chinese Science and Technology Cooperation Project #: 3-12
DOI
10.1080/02331934.2019.1647198
Citation Information
Fuzhen Zhang and Xiao-Dong Zhang. "Enumerating Extreme Points of the Polytopes of Stochastic Tensors: An Optimization Approach" Optimization Vol. 69 Iss. 4 (2020) p. 729 - 741 ISSN: 0233-1934 Available at: http://works.bepress.com/fuzhen-zhang/176/
©2019 Informa UK Limited, trading as Taylor & Francis Group