Information on the graduate course "Discrete and MixedInteger Optimization". There are no graduatelevel prerequisites for this course. In particular, it is completely independent of 258A "Numerical Optimization".Course Time / Room: see registrar's or department's class scheduleInstructor: Matthias KöppeOffice hours: see department office hours page Syllabus:Grading is based on homework (50%), a substantial final project (40%), and peergrading duties (10%).
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 selfstudy) are required.
Modeling techniques for integer and mixed integer optimization Modeling languages Optimization software Branchandcut 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 deviate from the syllabus where it makes sense to cover some recent developments Homework and other announcementsI will be using Canvas to announce reading, homework, and distribute grades.
Auditors: Please let me know your Kerberos id, so I can give you access to the Canvas site. Our textbooks: 1) Bertsimas, Weismantel: Optimization over the Integers, 600 pages, Hardcover, ca. $90 Should be available in the bookstore; no etext available unfortunately. 2) Michele Conforti, Gérard Cornuéjols, Giacomo Zambelli, Integer Programming, Graduate Text in Mathematics, Springer 2014, http://link.springer.com/book/10.1007%2F9783319110080I will supplement this by additional material on mixedinteger nonlinear optimization following the most recent developments on the research frontier. Other textbooks on integer optimization: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.
Additional reading:On Combinatorial Optimization:Combinatorial optimization is a subfield of discrete optimization, but not the emphasis in our class. 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 19582008: From the Early Years to the StateoftheArt, Hardcover, 804 pages
Among other things, this contains surveys on the most important current research directions in Integer and Nonlinear MixedInteger Optimization.
On MixedInteger Nonlinear Optimization and Global Optimization: Mohit Tawarmalani, Nikolaos V. Sahinidis, Convexification
and Global Optimization in Continuous and MixedInteger Nonlinear
Programming: Theory, Algorithms, Software, and Applications
 Christodoulos A. Floudas, Nonlinear and MixedInteger Optimization: Fundamentals and Applications
For a background on linear optimization:Most textbooks on linear optimization give sufficient background. Here are two examples:
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 retypeset version of this 1977 MIT classic is available online as a full text
Software COIN/OR, version 1.3.1 ("CoinAll" package)
This is installed on the Math computers in the directory ~mkoeppe/public/dest1.3.1/bin If you want to install this on your own computer, you can download a binary distribution from http://www.coinor.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/classaccts

