CS 525: Linear Programming - Spring 2011

Lecture: TuTh 2:30PM - 3:45PM
Location: Psychology 121
Mailing List: compsci525-1-s11@lists.wisc.edu (here's the archive).

Email Policy: I will respond to most questions about logistics and homework sent to the class mailing list. I will not repsond to any other emails. Questions about the course must be asked during office hours, during class, or on the class mailing list.

Instructor: Ben Recht
Office: 4387 CS
Office Hours: Tuesdays 1:30-2:30, Wednesdays 10-11

Teaching Assistant: Ji Liu
Office: 3393 CS
Office Hours:Mondays 3-4, Thursdays 10-11

Teaching Assistant: Srikrishna Sridhar
Office: 4352 CS
Office Hours:Wednesdays 2:30-3:30, Fridays 2:30-3:30

General Course Infromation

Linear programming is one of the most fundamental and practical problem classes in computational optimization. In this course, we take an algorithmic approach, describing the simplex algorithm and its variants, using Matlab to program the various elements of the algorithm. We discuss the concept of duality and its practical applications, and extensions to other important problem classes such as quadratic programming and linear complementarity problems. Applications such as classification problems and game theory are covered.

Course Outline

  • Linear Algebra Background
  • The Simplex Method
  • Duality
  • Revised Simplex Method
  • Interior Point Methods
  • Sensitivity Analysis
  • Approximation Problems
  • The Linear Complementarity Problem
  • Quadratic Programming

Prerequisites

  • Math 443 or 320 or 340 or consent of instructor.

Required Text:

References

  • V. Chvatal, Linear Programming, Freeman, New York, 1983.
  • G. B. Dantzig, Linear Programming with Extensions, Princeton University Press, Princeton, 1963.
  • S. J. Wright, Primal-Dual Interior-Point Methods, SIAM, 1997.
  • J. M. Ortega, Numerical Analysis: A Second Course, SIAM Classics in Applied Mathematics 3, SIAM, Philadelphia, 1990.
  • K. G. Murty, Linear Programming, Wiley, New York, 1983.
  • H. Karloff, Linear Programming, Birkhauser, Boston, 1991.
  • R. Saigal, Linear Programming, Kluwer, 1995.
  • M. N. Thapa and G. B. Dantzig, Linear Programming I: Introduction, Springer, 1997.

Assessment

Keep track of your grades through the learn@uw system. Log on, click through to the page for this course, and click the "Grades" tab at the top of the page.

  • Approximately one homework assignment per week, approximately 25% of grade in total.
    • The Dropbox facility of learn@uw will be used for some homeworks. You can access this by clicking the "Dropbox" tab at the top of the course page on learn@uw. Details of submission procedures will be indicated on each homework.
    • Homework is due at the beginning of class on the designated date.
    • No homeworks will be accepted by TAs, in mailbox or in person.
    • No homework or project is accepted in mailbox of instructor.
    • You may discuss homework with classmates, but the submitted version must be worked out, written, and submitted alone.
    • Submitting someone else's work as your own is academic misconduct. Cheating and plagiarism will be dealt with in accordance with University procedures (see this information on Academic Misconduct at UW-Madison).
    • Many assignments will require you to do Matlab programming using the Matlab routines described in the book. Here is some basic information about setting up your MATLAB environment for this course on the instructional CS linux machines.
  • CLASS PROJECT, 10% of grade. Due last week of class (details below). Submit in class or to professor's office.
  • MIDTERM, 25% of grade. Tuesday, March 8, 2011, 2:30-3:30 PM, Psychology 121. You may bring into the exam one page of handwritten notes (written both sides). No other books or notes, and no calculators or other electronic devices.
  • FINAL, 40% of grade. To be held on Sunday, May 8, 2011, from 7:45AM - 9:45AM. Location TBA. You may bring into the exam one page of handwritten notes (written both sides). No other books or notes, and no calculators or other electronic devices.

Lectures

The current lecture schedule is posted here. It's subject to modification. In particular, some lectures will be dropped or given by a guest lecturer. I'll make sure the schedule is accurate to at least a week in advance.

Week 1: Tu 1/18 (75 min - S. Wright), Th 1/20 (75 min - S. Wright)

Homework Assignments

  • Homework 1, for practice only; no submission required. Here is the data file hwk1.mat. (This file is also on the course public directory at ~cs525-1/public, which will be in your Matlab path if you're using the CS linux machines and if your path is set up correctly.)
  • Homework 2, due Feb 8, 2011.
  • Homework 3, due Feb 10, 2011.
  • Homework 4, due Feb 17, 2011.
  • Homework 5, due Feb 24, 2011.
  • Homework 6, FOR PRACTICE ONLY. You do not have to hand in this assignment, but it is good practice for the midterm.
  • Homework 7, due Mar 31, 2011.
  • Homework 8, due Apr 14, 2011.
  • Homework 9, due Apr 21, 2011.
  • Homework 10, due Apr 28, 2011.

Class Project: The Disputed Federalist Papers: Resolving the Dispute with Quadratic Programming.

(Due 5:00pm on May 12, 2010. No Late Submissions Accepted.)

Here is Fung's background paper, cited in the project description. I also recommend the Wikipedia entry about the Federalist Papers.

You will need to do the project on your CS unix account, as it requires access to CPLEX, which is installed on these machines (and probably not on your laptop). To enable calling of CPLEX from your Matlab programs, you need to add the following line to the .cshrc.local file in your home directory (creating this file if necessary): 

 setenv ILOG_LICENSE_FILE /s/cplex-9.1/license/access.ilm

In case your account uses the bash shell you should also add the following line to the file .bashrc.local in your home directory (creating this file if necessary):

 export ILOG_LICENSE_FILE=/s/cplex-9.1/license/access.ilm

Then logout and login again.

I suggest using the humboldt, macaroni, and king machines in the CS instructional labs. If you are using the mumble machines (which are 32-bit) you will need to invoke the 32-bit version of matlab, which you can do by typing "matlab -nojvm -glnx86"

Handouts and Examples

  • Introduction to MATLAB by Mark S. Gockenbach: html and postscript
  • The 3rd edition of Kermit Sigmon's Matlab Primer. The 7th edition of this book, by Timothy Davis and Kermit Sigmon, can be purchased online.
  • The DIET PROBLEM demo. Try it yourself!
  • A routine permcols.m to rearrange the columns in a tableau.

Past Exams and Solutions

Here are some previous midterm examinations:

Here are some previous final examinations:

Computing Information

Use the CS Unix Labs on the first floor of CS: Locations here.

For new users of Unix and the CS Unix facilities, orientation sessions will be held in CS&S 1325 early in the semester. Schedules will be posted in the lobby of the CS Building.

Here are some instructions for setting up your Matlab environment on the linux machines, if you have not done this before.