# Polyhedral Computation (Spring 2016)

## Contents

In this lecture, we study basic and advanced techniques for polyhedral computation in general dimension. We review some classical results on convexity and convex polyhedra such as polyhedral duality, Euler's relation, shellability, McMullen's upper bound theorem, the Minkowski-Weyl theorem, face counting formulas for arrangements. Our main goal is to investigate fundamental problems in polyhedral computation from both the complexity theory and the viewpoint of algorithmic design. Optimization methods, in particular, linear programming algorithms, will be used as essential building blocks of advanced algorithms in polyhedral computation. Various research problems, both theoretical and algorithmic, in polyhedral computation will be presented.

## Textbook