CS 525: Linear Programming

Fall 2009

Linear programming is one of the most fundamental and practical problem classes in computational optimizatio. 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 also discuss extensions to other important problem classes such as quadratic programming and linear complementarity problems. Important applications such as classification problems and game theory are also covered.

Schedule

Lecture:

11:00-11:50 MWF, 103 Psychology

Class Mailing List: compsci525-1-f09@lists.wisc.edu (here's the archive)
Mail Instructor/TAs
Course URL: http://www.cs.wisc.edu/~swright/cs525.html

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: Wed 9/2 (50 min), Fri 9/4 (50 min)
  • Week 2: Mon 9/7 (no lecture: Labor Day), Wed 9/9 (50 min), Fri 9/11 (50 min)
  • Week 3: Mon 9/14 (50 min), Wed 9/16 (50 min), Fri 9/18 (50 min)
  • Week 4: Mon 9/21 (50 min), Wed 9/23 (50 min), Fri 9/25 (50 min)
  • Week 5: Mon 9/28 (50 min: Daniel Myers), Wed 9/30 (no lecture), Fri 10/2 (50 min)
  • Week 6: Mon 10/5 (50 min), Wed 10/7 (50 min), Fri 10/9 (50 min)
  • Week 7: Mon 10/12 (50 min), Wed 10/14 (50 min), Fri 10/16 (50 min)
  • Week 8: Mon 10/19 (50 min), Wed 10/21 (50 min), Fri 10/23 (50 min)
  • Week 9: Mon 10/26 (50 min) (MIDTERM 7:15pm-9:15pm), Wed 10/28 (no lecture), Fri 10/30 (50 min)
  • Week 10: Mon 11/2 (50 min), Wed 11/4 (50 min), Fri 11/6 (50 min: Daniel Myers)
  • Week 11: Mon 11/9 (50 min), Wed 11/11 (50 min), Fri 11/13 (50 min: Daniel Myers)
  • Week 12: Mon 11/16 (50 min), Wed 11/18 (50 min), Fri 11/20 (50 min)
  • Week 13: Mon 11/23 (50 min), Wed 11/25 (50 min), Fri 11/27 (no lecture: Thanksgiving break)
  • Week 14: Mon 11/30 (50 min), Wed 12/2 (50 min), Fri 12/4 (50 min)
  • Week 15: Mon 12/7 (50 min), Wed 12/9 (50 min), Fri 12/11 (absent)
  • Week 16: Mon 12/14 (50 min)

 

Instructor: Stephen Wright

Office: 4379 CS
Phone: 262-4838
Email:
Office Hours: Tuesday 1-2, Friday 9:30-10:30

Teaching Assistant: Taedong Kim

Office: 1307 CS
Email:
Office Hours: Monday 3-4, Thursday 1-2

 

Teaching Assistant: Daniel Myers

Office: 4378 CS
Email:
Office Hours: Tuesday 3-4

 

General Course Information

Prerequisites

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

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.

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

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, 30% 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).
  • CLASS PROJECT, 10% of grade. Due on Monday Dec 14, 2009 at 5:00pm. (Submit in class or to professor's office.)
  • MIDTERM, 20% of grade. Monday Oct 26, 2009, 7:15pm-9:15pm, Room B130, Van Vleck Hall. 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 Monday Dec 21, 2009, 10:05a-12:05p, Location: PSYCHOLOGY 113. 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.

 

Past Exams and Solutions

Here are some previous midterm examinations:

Here are some previous final examinations:

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, hard copy due in class on Friday 9/18/09.
  • Homework 3, hard copy due in class on Friday 9/25/09.
  • Homework 4, hard copy due in class on Monday 10/5/09.
  • Homework 5, hard copy due in class on Wednesday 10/14/09.
  • Homework 6, hard copy due in class on Wednesday 10/21/09.
  • Homework 7, hard copy due in class on Monday 11/9/09.
  • Homework 8, hard copy due in class on Wednesday 11/18/09. You can find the code rsm.m on this page.
  • Homework 9, hard copy due in class on Monday 11/23/09.

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

(Due on Dec 14, 2009 at 5:00pm.)

(The last two files are also available on the course web site ~/cs525-1/public.)

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 root directory: 

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

Then logout and login again.

Computing Information

Use the CS Unix Labs on the first floor of CS&S: Locations here. Information that's particularly helpful for first-time users can be found here.

For new users of Unix and the CS Unix facilities, orientation sessions will be held in CS&S 1325 according to the following schedule.

Here is some basic information about setting up your MATLAB environment for this course. In particular, there are instructions for setting up a startup file that defines a search path for Matlab that includes the public directory for the course.

 

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.
  • Using phase I-phase II simplex to solve the primal and dual problems simultaneously, for the problem of Section 4.3.
  • Example of revised simplex applied "manually" to a problem with upper and lower bounds: rsm-bounded.txt

Miscellaneous