Course Time / Room: see registrar's or department's class schedule
Instructor: Matthias Köppe
Office hours: see department office hours page
Grading is based on homework (70%) and a substantial final project (30%). Solving homework will require ability to read and write mathematical proofs, and familiarity with a programming language of your choice. Knowledge of linear algebra and the basics of linear optimization (see below for resources on linear optimization for self-study) are required.
Topics:
Modeling techniques for integer and mixed integer optimization
Modeling languages
Optimization software
Branch-and-cut technology for combinatorial and mixed integer linear optimization
Cutting plane theory
Primal methods
Nonlinear branch and bound and outer approximation
Global optimization: Spatial branch and bound and convexification
I will be using SmartSite to announce reading, homework, and distribute grades.
Auditors: Please let me know your Kerberos id, so I can give you access to SmartSite.
Bertsimas, Weismantel: Optimization over the Integers, 600 pages, Hardcover, ca. $90
Should be available in the bookstore.
Our textbook is a very up-to-date (2005), comprehensive, and accessible textbook that covers all aspects of integer and mixed-integer linear programming. It is used at MIT and other places for teaching Integer Programming at the graduate level.
I will supplement this by additional material on mixed-integer nonlinear optimization following the most recent developments on the research frontier.
On Combinatorial Optimization:
Combinatorial optimization is a subfield of discrete optimization, but not the emphasis in our class.
On Integer Optimization:
On Mixed-Integer Nonlinear Optimization and Global Optimization:
For a background on linear optimization:
Most textbooks on linear optimization give sufficient background. Here are two examples:
Further resources:
Software
If you don't have an account on the Math computers, you can request a class account by visiting http://www.math.ucdavis.edu/comp/class-accts