Math 482: Linear Programming (Spring 2019)

Mikhail Lavrov



The course grade will be calculated as follows, out of 660 points total:

You can check your grades via Moodle.

Your grade total will be converted to a letter grade according to the following scale:

A+ ≥ 630 B+ ≥ 520 C+ ≥ 450 D+ ≥ 380
A ≥ 570 B ≥ 490 C ≥ 420 D ≥ 350
A- ≥ 540 B- ≥ 470 C- ≥ 400 D- ≥ 330

It is possible to take the course for 4 credits rather than 3, at the cost of extra homework questions and more difficult exams. If you want to do this, you need to register at the math office in Altgeld Hall soon after the start of the course.


There will be 10 homework assignments, to be turned in at the beginning of class the day they are due. Of these homework assignments, the top 8 homework scores will determine your grade. Each assignment is graded out of 20 points, for a total of 160.

If you cannot attend class, you can submit a scanned copy or a photo of your homework as a PDF file by e-mail before class begins. Please avoid doing this unless it's necessary, since it is more work for the grader.

If the homework assignment is received after class on the due date, but before the next class, it will be accepted as late, for a 2-point penalty. Homework will not be accepted after the next class for any reason.


There will be three evening midterm exams: Wednesday 2/13, Wednesday 3/13, and Wednesday 4/17 from 7pm to 8:30pm in 341 Altgeld Hall. Correspondingly, three lectures will be canceled, not necessarily in the same week as the midterm exams. The first of these is already marked in the syllabus below.

The final exam will be on Monday 5/6 from 7pm to 10pm in 311 Gregory Hall (our usual classroom).

Detailed syllabus

This course is based on several textbooks with a lot of overlap; read whichever ones help. In the syllabus, I will refer you to sections of the textbooks below that cover the relevant material.

The syllabus below will initially describe a tentative plan for what topics will be covered when. As the semester progresses, I will update the syllabus with information about what actually happened in class, adjustments to my plans for the future, and links to homework assignments.

Date Chapter Details References Homework/Exams
Mon January 14 Background
PS Chapter 1
Intro to linear programs GM 1.1
Wed January 16 LPs in different forms GM 4.1; PS 2.1
Fri January 18 No class
Mon January 21 MLK Day: no class
Wed January 23 Convex geometry GM 4.3-4.4; PS 1.5, 2.3
Fri January 25 The Simplex Method
PS Chapter 2
Basic solutions; pivoting GM 4.2; PS 2.2, 2.4 HW 1 due
Mon January 28 Objective functions GM 5.1; PS 2.5, 2.6
Wed January 30 Extreme (temperature) point day: no class
Fri February 1 Simplex method example GM 5.2, 5.3; PS 2.9 HW 2 due
Mon February 4 Two-phase simplex method GM 5.4, 5.6; PS 2.8
Wed February 6 Pivot rules and cycling GM 5.7, 5.8; PS 2.7
Fri February 8 Proofs and notation GM 4.2, 5.5; PS 2.2 HW 3 due
Mon February 11 Revised simplex method GM 5.6; PS 4.1, 4.2
Wed February 13 Simplex method review Exam: 7pm in 341 AH (Topics)
Fri February 15 Counting pivot steps GM 5.9; PS 8.6
Mon February 18 Duality
PS Chapter 3
Intro to duality PS 3.1, GM 6.1-6.2, V 5.1-5.4
Wed February 20 Complementary slackness PS 3.2, GM 6.4, V 5.5
Fri February 22 Duality in the tableau PS 3.5, GM 6.3 HW 4 due
Mon February 25 Dual simplex method PS 3.6-3.7, V 5.6
Wed February 27 Shadow costs
Fri March 1 Sensitivity analysis V 7.1.1 HW 5 due
Mon March 4 Zero-sum games GM 8.1
Wed March 6 Zero-sum games GM 8.1
Fri March 8 No class
Mon March 11 Other topics Fourier-Motzkin elimination GM 6.7 HW 6 due
Wed March 13 Exam review Exam: 7pm in 341 AH (Topics)
Fri March 15 Applications GM 2.4, 2.6
Mon March 18Spring break: no class
Wed March 20
Fri March 22
Mon March 25 Graph Theory Totally unimodular matrices GM 8.2
Wed March 27 Matchings and vertex covers GM 8.2, PS 10.1
Fri March 29 Network flows V 15.5 HW 7 due
Mon April 1 Max-flow min-cut thorem V 15.5
Wed April 3 Augmenting paths PS 5.6??
Fri April 5 Ford-Fulkerson PS 6.1-6.2 HW 8 due
Mon April 8 Extensions of max-flow external slides
Wed April 10 Push-relabel external notes
Fri April 12 More push-relabel HW 9 due
Mon April 15 Integer Programming
PS Chapter 13
The power of integer programs PS 13.1, CCZ 1.1
Wed April 17 Exam review Exam: 7pm in 341 AH (Topics)
Fri April 19 The branch-and-bound method PS 18.1, V 23.5, CCZ 1.2.1
Mon April 22 The cutting plane method CCZ 1.2.2
Wed April 24 Primal-Dual Method
PS Chapter 5
The primal-dual method PS 5.1, 5.2
Fri April 26 More primal-dual method PS 5.3, example
Mon April 29 Solving the restricted primal PS 5.2 HW 10 due
Wed May 1 Exam review (optional)
Mon May 6 Final Exam (Topics)

Last updated May 3, 2019. Mikhail Lavrov <>