(Nonlinear) Integer Programming 097334

The course develops an algorithmic theory of (nonlinear) integer programming and its many applications, with an emphasis on very recent developments, recalling on the way necessary background from algebra, geometry, complexity and optimization as needed. The main prerequisite is mathematical maturity. Most of the material is drawn from two sources:

• Survey article (for the IMA Volume on Mixed Integer Nonlinear Programming, Springer Frontier Series, 2009): Theory and Applications of N-Fold Integer Programming

• Monograph (will be available to participants) and preliminary Nachdiplom Lecture Notes (given at ETH Zurich, Spring 2009): Nonlinear Discrete Optimization

Nonlinear Discrete Optimization: An Algorithmic Theory.

Contents

1. Introduction

           Homework 1 (due March 22, 14:30)

2. Convex Discrete Maximization

3. Nonlinear Integer Programming

4. N-Fold Integer Programming

5. Multiway Tables and Universality

6. Nonlinear Combinatorial Optimization

References and Index