Add to ORKGConsidering n × n × n stochastic tensors (aijk)(i.e., nonnegative hypermatrices in which every sum over one index i, j, or k, is 1), we study the polytope (Ωn) of all these tensors, the convex set (Ln) of all tensors in Ωn with some positive diagonals, and the polytope (Δn) generated by the permutation tensors. We show that LnLn is almost the same as Ωn except for some boundary points. We also present an upper bound for the number of vertices of Ωn
Let Ωn be the set all of n × n doubly stochastic matrices. It is well-known that Ωn is a polytope wh...
Let Ωn be the set all of n × n doubly stochastic matrices. It is well-known that Ωn is a polytope wh...
In this paper, we consider the symmetric and Hankel-symmetric transportation polytope Ut&h(R,S), whi...
We begin with the definition of a tensor (in algebra) and then focus on the tensors by which we mean...
This paper studies lower and upper bounds for the number of vertices of the polytope of n x n x n st...
This paper is concerned with the extreme points of the polytopes of stochastic tensors. By a tensor ...
In optimization theory, many problems involve functions defined on convex sets, most of which are po...
In optimization theory, many problems involve functions defined on convex sets, most of which are po...
AbstractWe consider the convex polytope Sn(x) that consist of those n×n (row) stochastic matrices ha...
The purpose of this volume is to give an up-to-date introduction to tensor valuations and their appl...
AbstractLet x and y be positive vectors in Rn. The set of all n × n nonnegative matrices having x an...
We investigate convex polytopes of doubly stochastic matrices having special structures: symmetric, ...
AbstractWe investigate the extreme points, faces and their dimensions of the convex polytope of doub...
Let Ωn denote the convex polyhedron of all nxn d.s. (doubly stochastic) matrices. The main purpose ...
Let Ωn denote the convex polyhedron of all nxn d.s. (doubly stochastic) matrices. The main purpose ...
Let Ωn be the set all of n × n doubly stochastic matrices. It is well-known that Ωn is a polytope wh...
Let Ωn be the set all of n × n doubly stochastic matrices. It is well-known that Ωn is a polytope wh...
In this paper, we consider the symmetric and Hankel-symmetric transportation polytope Ut&h(R,S), whi...
We begin with the definition of a tensor (in algebra) and then focus on the tensors by which we mean...
This paper studies lower and upper bounds for the number of vertices of the polytope of n x n x n st...
This paper is concerned with the extreme points of the polytopes of stochastic tensors. By a tensor ...
In optimization theory, many problems involve functions defined on convex sets, most of which are po...
In optimization theory, many problems involve functions defined on convex sets, most of which are po...
AbstractWe consider the convex polytope Sn(x) that consist of those n×n (row) stochastic matrices ha...
The purpose of this volume is to give an up-to-date introduction to tensor valuations and their appl...
AbstractLet x and y be positive vectors in Rn. The set of all n × n nonnegative matrices having x an...
We investigate convex polytopes of doubly stochastic matrices having special structures: symmetric, ...
AbstractWe investigate the extreme points, faces and their dimensions of the convex polytope of doub...
Let Ωn denote the convex polyhedron of all nxn d.s. (doubly stochastic) matrices. The main purpose ...
Let Ωn denote the convex polyhedron of all nxn d.s. (doubly stochastic) matrices. The main purpose ...
Let Ωn be the set all of n × n doubly stochastic matrices. It is well-known that Ωn is a polytope wh...
Let Ωn be the set all of n × n doubly stochastic matrices. It is well-known that Ωn is a polytope wh...
In this paper, we consider the symmetric and Hankel-symmetric transportation polytope Ut&h(R,S), whi...