INTEGER PROGRAMMING - IEOR 6605x

Spring 2013

MW 1:10-2:25

Lecturer: Professor Daniel Bienstock. Office hours: by appointment

Recommended Textbook: A. Schrijver, Theory of Linear and Integer Programming

Prerequisite: doctoral-level Linear Programming

Course Outline

1. Theory of lattices and linear diophantine equations
    a. Integer lattices and the Hermite normal form of a matrix
    b. Diophantine approximation and basis reduction in lattices

2. Basic theory
    a. Structure of integral solutions to linear systems of inequalities
    b. Lenstra's algorithm for integer programming in fixed dimension
    c. Totally unimodular matrices
    d. Total dual integrality

3. Cutting Planes
    a. Gomory-Chvatal cutting planes and rank of polyhedra
    b. Mixed-integer cutting planes (MIR inequalities, split cuts)
    c. The disjunctive method, the Lovasz-Schrijver and Sherali-Adams reformulation procedures

This is a theoretical course focusing of fundamental topics in modern integer programming. The course will be based on lectures by the instructor, with homework projects involving proofs. The course will also include a comprehensive survey of linear programming.

Materials

INTEGER PROGRAMMING - IEOR 6605x

Course Outline

Last revised: January 4 2013