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CS/ISyE/Stat/Math 525 - Spring 2017
Linear Programming
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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.
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Schedule
In general, there will be three 60-minute lectures each week, starting at 8:40am and finishing at 9:40am. The start is 10 minutes eariler than the time in the official schedule. By extending most lectures to 60 minutes, we can cancel about 5 classes during semester as needed.
The current lecture schedule is posted here. The schedule is subject to modification. In particular, some lectures will be given by guest lecturers, or cancelled.
- Week 1: 1/18 (50 min), 1/20 (50 min)
- Week 2: 1/23 (50 min), 1/25 (50 min), 1/27 (50 min)
- Week 3: 1/30 (60 min), 2/1 (60 min), 2/3 (60 min)
- Week 4: 2/6 (60 min), 2/8 (60 min), 2/10 (NO CLASS)
- Week 5: 2/13 (60 min), 2/15 (60 min), 2/17 (60 min)
- Week 6: 2/20 (60 min), 2/22 (60 min), 2/24 (60 min)
- Week 7: 2/27 (60 min), 3/1 (60 min), 3/3 (60 min)
- Week 8: 3/6 (60 min), 3/8 (60 min), 3/10 (60 min)
- Week 9: 3/13 (60 min), 3/15 (60 min), 3/17 (60 min)
- SPRING BREAK
- Week 10: 3/27 (60 min), 3/29 (60 min), 3/31 (60 min)
- Week 11: 4/3 (60 min), 4/5 (60 min), 4/7 (60 min)
- Week 12: 4/10 (60 min), 4/12 (60 min), 4/14 (60 min)
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Office: |
4379 CS |
Phone: |
262-4838 |
Email: |
swright at cs
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Office Hours: |
Mon 3-4, Thu 3-4 |
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Teaching Assistant: Qisi Wang
Office: |
1308 CS |
Email: |
qisi.wang at wisc
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Office Hours: |
Wed 2-3, Thu 10-11 |
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Teaching Assistant: Huilin Hu
Office: |
3363 CS |
Email: |
hhu28 at wisc
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Office Hours: |
Wed 3-4 |
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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.
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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
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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.
- Homeworks will be assigned through the Piazza page.
- 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. (Most of you will probably use your own local version of Matlab.)
CLASS PROJECT, 10% of grade. Due last week of class (details below). Submit in class or to professor's office.
MIDTERM, 25% of grade. To be held on Wednesday, 15 March 2017, 7:15pm-9:15pm, 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.
FINAL, 40% of grade. To be held on 10 May 2017, 10:05am-12:05pm, Location:Chamberlin 2241.
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.
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Past Exams and Solutions
Here are some previous midterm examinations:
Here are some previous final examinations:
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Final exam from Spring 1997 and
Solutions for Q1, Q2, Q3, Q5
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Final exam from Fall 1999 and
Solutions for Q1, Q2, Q3
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Final exam from Spring 2000 and
Solutions
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Final exam from Fall 1996 and
Solutions
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Final exam from Spring 1996 and
Solutions
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Final exam from Spring 1998 and
Solutions
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Final exam from Spring 1999 and
Solutions
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Final exam from Spring 2002 and
Solutions
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Final exam from Spring 2003 and
Solutions
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Final exam from Spring 2004 and
Solutions
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Final exam from Spring 2005 and
Solutions
- Final exam from Spring 2008 and Solutions (average: 85/100, median: 92/100)
- Final exam from Spring 2009 and Solutions (average: 52/80, median: 54.5/80)
- Final exam from Fall 2009 and Solutions
(average: 74.5/100, median: 75/100)
- Final exam from Fall 2010 and Solutions (average: 57/80, median: 59/80)
- Final exam from Fall 2012 and Solutions (average: 57/80, median: 61/80)
- Final exam from Spring 2014 and Solutions (average: 55/80, median: 54/80). Here is an alternative solution for Q2.
- Final exam from Fall 2014 and Solutions (average: 18/26, median: 18/26).
- Final exam from Fall 2015 (mean: 29.5/39).
- Final exam from Spring 2017 (mean: 19.5/29).
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Computing Information
Use the CS Unix Labs on the first floor of Computer Sciences.
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.
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Handouts and Examples
- Introduction to MATLAB by Mark S. Gockenbach: html and postscript
- The 3rd edition of Kermit Sigmon's Matlab Primer. Later editions 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
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Miscellaneous
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