Preliminary information on the graduate course "Discrete and Mixed-Integer Optimization".
More information will appear here shortly.
258B is still listed with the old title "Variational Analysis" in the course catalog.
The new 258B has a completely changed syllabus (see below).
There are no graduate-level prerequisites for this course. In particular, it is completely independent of 258A "Numerical Optimization".
This course will be very different from 258A "Numerical Optimization".
Course Time: Tuesdays and Thursdays 1:40-3:00
Room: TBA
Instructor: Matthias Köppe
Office hours: TBA
Grading is based 100% on homework. 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 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
Detailed syllabus
Homework and other announcements
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.
- Laurence A. Wolsey, George L. Nemhauser, Integer and Combinatorial Optimization, 763 pages, Paperback, ca. $110
- A comprehensive, older (1988) text.
- Laurence A. Wolsey, Integer Programming, 264 pages, ca. $90-$130
- A gentle, and short, introduction to Integer Optimization aimed at the advanced undergraduate and master's level.
On Combinatorial Optimization:
Combinatorial optimization is a subfield of discrete optimization, but not the emphasis in our class.
- William J. Cook, William H. Cunningham, William R. Pulleyblank, Alexander Schrijver, Combinatorial Optimization
- Christos H. Papadimitriou, Kenneth Steiglitz, Combinatorial Optimization: Algorithms and Complexity
- A true classic. You can get a paperback of this one for ca. $14
- Bernhard Korte, Jens Vygen, Combinatorial optimization theory and algorithms, Springer, 2008
- Available through the UC Library as an e-text free of charge. (If you connect from off-campus, use the UC Library VPN.) You can also order a copy via SpringerLink for $25.
On Integer Optimization:
- Alexander Schrijver,Theory of Linear and Integer Programming, ca. $100
- An important reference for every researcher in Integer Optimization
- Michael Jünger, Thomas M. Liebling, Denis Naddef, George L. Nemhauser, William R. Pulleyblank, Gerhard Reinelt, Giovanni Rinaldi, Laurence A. Wolsey (Editors): 50 Years of Integer Programming 1958-2008: From the Early Years to the State-of-the-Art, Hardcover, 804 pages
- Among other things, this contains surveys on the most important current research directions in Integer and Nonlinear Mixed-Integer Optimization.
On Mixed-Integer Nonlinear Optimization and Global Optimization:
- Duan Li, Xiaoling Sun, Nonlinear integer programming, Springer, 2006.
- Available through the UC Library as an e-text free of charge. (If you connect from off-campus, use the UC Library VPN.) You can also order a copy via SpringerLink for $25.
- Ivo Nowak, Relaxation and decomposition methods for mixed integer nonlinear programming, Birkh?user, 2006.
- Available through the UC Library as an e-text free of charge. (If you connect from off-campus, use the UC Library VPN.) You can also order a copy via SpringerLink for $25.
- Mohit Tawarmalani, Nikolaos V. Sahinidis, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications
- Christodoulos A. Floudas, Nonlinear and Mixed-Integer Optimization: Fundamentals and Applications
For a background on linear optimization:
Most textbooks on linear optimization give sufficient background. Here are two examples:
- Introduction to Linear Optimization by Dimitris Bertsimas and John N. Tsitsiklis
- Linear Programming: Foundations and Extensions by Robert Vanderbei
Further resources:
- Bradley, Hax, Magnanti: Applied Mathematical Programming
- A general introduction to mathematical optimization, including integer linear optimization, from an applied point of view. This is a bit dated (1977), but still a good reading on the basic material.
- A re-typeset version of this 1977 MIT classic is available online as a full text
- COIN/OR, version 1.3.1 ("CoinAll" package)
- This is installed on the Math computers in the directory ~mkoeppe/public/dest-1.3.1/bin
- If you want to install this on your own computer, you can download a binary distribution from http://www.coin-or.org/download/binary/CoinAll/
- IBM ILOG CPLEX 12.1
- This is installed on the Math computers, and is available as the command cplexte
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