论文标题
列举随机张量的多面体的极端点：优化
Enumerating extreme points of the polytopes of stochastic tensors: an optimization approac
论文作者
论文摘要
本文涉及随机张量的多面点的极端点。通过张量，我们是指实数字段上的多维数组。线条张量是一种非负张量，其中每条线上所有条目的总和（即一个自由索引）等于1；平面 - 缝合张量是一种非负张量，其中每个平面上的所有条目的总和（即两个自由指标）等于1。在枚举订单3和维度3 $的线和平面 - 孔隙张量$ n $的多面体的极端点时，我们会通过线性优化和新的下部和上限来考虑方法。我们还研究了定义多型的系数矩阵。
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.
