CS 525: Linear Programming Methods -Fall 2005
(also IE 525, Math 525, Stat 525)

Schedule

  Lecture:    9:30-10:45 TR, Room 1221, CS&S Building, 1210 W Dayton.
  Archive of Class Mailing List
  Email to Instructor and TAs
  Course URL: http://www.cs.wisc.edu/~cs525-1 

Instructor: Robert Meyer

  Office:       4385 CS&S
  Office Hours: Wed 2:00-3:00, Fri 2:00-3:00

Teaching Assistants:

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  Office:        CS&S
  Office Hours: 

General Course Information

Overview

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

Text

We use MATLAB extensively in this course. This MATLAB Primer (postscript file, 40pp. approx) will be useful if you have no prior experience with MATLAB.

Here is a zip file and a tar.gz file with most of the contents of the directory ~cs525-2/public, including the m-files of routines referred to in the notes and .mat files containing data for many of the problems.. This may be useful to those of you who wish to run the homeworks and examples on your own Windows PC with Matlab, instead of on the CS Unix environment.

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.

Prerequisites

Important Dates

• Tuesday, September 6: First class
• Midsemester: Midterm exam (held in class, open book)
• Last Class. Class Project Due
• Thursday, Dec 22, 2:25p-4:25p: Final Exam

Grading

• Approximately: 30% Homework, 25% Midterm, 35% Final, 10% Project
• Approximately seven homework assignments. Most of the assignments will require the use of MATLAB, which will also be used extensively in the lectures.
  • Homework is due at the beginning of class. Homework will be collected soon after 9:30. A 50% late penalty will then apply until the end of class, and a 100% late penalty will apply after that. All homework assignments will be equally weighted, and the lowest homework grade will be deleted.
    
  • No homeworks will be accepted by TAs,either in the TA  mailbox or in person.
  • No homework or project is accepted in mailbox of instructor.

Handouts

• Getting Started in MATLAB: A description of everything you need to do to get set up to use Matlab in this course.
• Interpretation of the dual linear program: An Example.
• pdip.m: primal-dual interior-point code.
• An exercise to test your knowledge of Section 6.1.
• Phase I problem for parametrized right-hand side, to determine a value of parameter t for which the problem with right-hand side b+th is feasible.

Handouts from DoIT:

• 525 Handout 1. Class text, Linear Programming via MATLAB, available from DoIT.

Previous Programming Assignments and Homeworks (from last semester)

• Homework 1: pdf, (due January 28) (average: 24/25)
• Homework 2: pdf, (due February 4)
• Homework 3: pdf, (due February 11)
• Homework 4: pdf, (due February 18)
• Homework 5: pdf, (due February 25)
• Homework 6: pdf, (due March 3)
• Homework 7: pdf, (due March 11). Here is the solution
• Homework 8: pdf, (due Monday April 4)
• Homework 9: pdf, (due Wednesday April 13) (Solution files here: Q1a, Q1b, Q2, Q3.)
• Homework 10: pdf, (due Wednesday April 20)
• Homework 11: pdf, (due Wednesday April 27)
• Homework 12: pdf, (due May 2).

Class Project

• Project: pdf.
• wdbc.data
• wdbc.names
• wdbcData.m

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 CPLEXLICENSE /s/cplex-6.6/cplexlicfile

Examinations

The final exam is open book. Calculators and computers are NOT allowed.

Here are some previous midterm examinations:

• Spring 1997: Part 1, Part 2 (done over two consecutive 50-min classes). MATLAB solution.
• Spring 1998: Exam. MATLAB solution.
• Fall 1998: Exam. MATLAB solution.
• Spring 1999: Exam. MATLAB solution.
• Fall 1999: Part 1, Part 2 . MATLAB solution.
• Spring 2000: Exam. MATLAB solution.
• Spring 2001: Part 1, Part 2 . MATLAB solution.
• Spring 2002: pdf and Solution.
• Spring 2003: pdf and Solution
• Spring 2004: pdf and Solution and grading scheme. (average: 86/100; median 89/100)
• Spring 2005: Part I and Part II, and the Solution. (average: 80.4; median: 86.5)

Here are some previous final examinations:

• Final exam from Spring 1997 and Solutions for Q1, Q2, Q3, Q5
• Final exam from Fall 1999 and Solutions for Q1, Q2, Q3
• Final exam from Spring 2000 and Solutions
• Final exam from Fall 1996 and Solutions
• Final exam from Spring 1996 and Solutions
• Final exam from Spring 1998 and Solutions
• Final exam from Spring 1999 and Solutions
• Final exam from Spring 2002 and Solutions
• Final exam from Spring 2003 and Solutions
• Final exam from Spring 2004 and Solutions

Miscellaneous

• NEOS Guide: Simplex Tool
• Archive of Class Mailing List
• Computer Systems Laboratory documentation
  • Computer Systems Laboratory FAQ
  • Unix Orientation Sessions
  • Instructional Facilities
  • Account Activation
  • Instructional Account Policies
  • Forwarding Email
• Introduction to UNIX at UW
• Introduction to MATLAB by Mark Gockenbach.
• Getting Started in MATLAB for this course
• Optimization at UW, including Courses related to 525.