CS/ISyE/Stat/Math 525 - Fall 2014

Linear Programming

 

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.

 
 

Schedule

Lecture:

11:00-11:50 MWF, Engineering Hall 2535
Class Mailing List: compsci525-1-f14@lists.wisc.edu (here's the archive)
Mail Instructor / TA mail to cs525-1 (at cs) should reach instructor and TA
Course URL: http://www.cs.wisc.edu/~swright/cs525-f14.html

The current lecture schedule is posted here. Unless otherwise specified, lectures are from 11:00am-11:50am on the specified date. The schedule is subject to modification. In particular, some lectures will be given by a guest lecturer, or cancelled.

  • Week 1: 9/3 (Guest lecturer: Prof M. Ferris), 9/5
  • Week 2: 9/8, 9/10, 9/12
  • Week 3: 9/15, 9/17, 9/19
  • Week 4: 9/22, 9/24, 9/26
  • Week 5: 9/29, 10/1, 10/3
  • Week 6: 10/6 (Guest lecturer: Dr Jagdish Ramakrishnan), 10/8 (Guest lecturer: Dr Ramakrishnan), 10/10
  • Week 7: 10/13, 10/15, 10/17
 

Instructor: Stephen Wright

Office: 4379 CS
Phone: 262-4838
Email: swright at cs
Office Hours: Mon 3-4, Thu 4-5
 
 

Teaching Assistant: Ian Skoch

Office: 1308 CS
Email: iskoch at cs
Office Hours: Wed 2-3, Thu 2-3

 
 
 

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, approximately 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).
    • 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, 20% of grade. To be held on Monday October 27, 7:15pm, Location: Chemistry B371. 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 Wednesday Dec 17, 2014, 12:25p-2:25p, Location:Computer Sciences 1221. 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.

 
 
 

Homework Assignments

  • Homework 1, for practicing Matlab and CVX; do not submit. 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 9/12/14.
  • Homework 3, hard copy due in class on Friday 9/19/14.
  • Homework 4, hard copy due in class on Friday 9/26/14.
  • Homework 5, hard copy due in class on Friday 10/3/14.
  • Homework 6, hard copy due in class on Friday 10/10/14.
  • Homework 7, hard copy due in class on Friday 10/17/14.
  • Homework 8, hard copy due in class on Monday 11/3/14.
  • Homework 9, hard copy due in class on Monday 11/10/14.
  • Homework 10, hard copy due in class on Friday 11/14/14.
  • Homework 11, hard copy due in class on Monday 11/24/14.
  • Homework 12, hard copy due in class on Friday 12/5/14.
 
 

Past Exams and Solutions

Here are some previous midterm examinations:

Here are some previous final examinations:

 
 

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

Posted 10 November 2014. Due 5:00pm on Friday 12 December 2014. No Late Submissions Accepted.

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

Here is Fung's background paper on this problem. I also recommend the Wikipedia entry about the Federalist Papers.

Since we are using Matlab and CVX for this project, most of you can probably run it on your own computers. But you may use the computers in the CS Lab if you need to.

 
 

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.
  • 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
  • Solving QPs in nonstandard form using "Scheme II" pivots and Lemke's method: handout_lcp.pdf
 
 

Miscellaneous