Polytopes and Matrix Equations

Fuzhen Zhang

Polytopes and Matrix Equations

Fuzhen Zhang

Department of Mathematics

Research output: Contribution to conference › Presentation

Abstract

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.

Original language	American English
State	Published - Aug 17 2017
Event	Third Pacific Rim Mathematical Association Congress - Oaxaca, Mexico Duration: Aug 14 2017 → Aug 18 2017 Conference number: 3

Conference

Conference	Third Pacific Rim Mathematical Association Congress
Country/Territory	Mexico
City	Oaxaca
Period	8/14/17 → 8/18/17

Disciplines

Mathematics

Access to Document

http://gaspacho.matmor.unam.mx/special-sessions/talk/36

Cite this

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title = "Polytopes and Matrix Equations",

abstract = " 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.",

author = "Fuzhen Zhang",

year = "2017",

month = aug,

day = "17",

language = "American English",

note = "Third Pacific Rim Mathematical Association Congress ; Conference date: 14-08-2017 Through 18-08-2017",

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TY - CONF

T1 - Polytopes and Matrix Equations

AU - Zhang, Fuzhen

N1 - Conference code: 3

PY - 2017/8/17

Y1 - 2017/8/17

N2 - 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.

AB - 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.

UR - https://nsuworks.nova.edu/cnso_math_facpres/368

UR - http://gaspacho.matmor.unam.mx/special-sessions/talk/36

M3 - Presentation

T2 - Third Pacific Rim Mathematical Association Congress

Y2 - 14 August 2017 through 18 August 2017

ER -

Polytopes and Matrix Equations

Abstract

Conference

Disciplines

Access to Document

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