Polytopes and Matrix Equations
Third Pacific Rim Mathematical Association Congress, Oaxaca, Mexico, August 14-18, 2017
In optimization theory, many problems involve functions defined on convex sets, most of which are polytopes (a convex set generated by a finite set of points). These polytopes may defined by a set of matrix (inequalities) equations (for example, the Birkhoff polytope). We will consider the polytopes of (line or plane) stochastic tensors, show the roles of matrix equations (hyperplanes) in the study. In particular, we will present an upper bound for the number of vertices of the polytope of the plane stochastic tensors.
Zhang, Fuzhen, "Polytopes and Matrix Equations" (2017). Mathematics Faculty Proceedings, Presentations, Speeches, Lectures. 368.