Course Page

Convex Polytopes

Course Number:

47861


Program

PHD


Concentrations

Operations Research or Statistics


Course Description

Basic results on inequalities: Fourier-Motzkin elimination, Farkas  Lemma, Theorems of the Alternative Faces of  polyhedra: vertices, facets, the face lattice; polarity; representation of polytopes and polyhedra

Projection of polyhedra: restricton versus projection, projection cone, projection with a minimal system of inequalities

Monotonization of polyhedra: dominants, submissives, relations between their facets

Extended formulation, lifting and projection: comparing formulations

Unions of polyhedra,  disjunctive programming, sequential convexification

Hyperplane arrangements

Format

Lecture: 100min/wk and Recitation: 50min/wk


Pre-requisites

None