Math 484: Nonlinear Programming (Fall 2017)

Mikhail Lavrov


Location

Grading

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:

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.

Homework

There will be at least 9 (most likely 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 by e-mail before class begins.

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.

Exams

There will be three in-class midterm exams (graded out of 100 points each) on the following dates:

The final exam will be given on Friday, December 15, 8:00-11:00am, in 241 Altgeld Hall.

Detailed syllabus

The course follows the textbook The Mathematics of Nonlinear Programming by A. Peressini, F. Sullivan and J. Uhl. The syllabus below will initially describe a tentative plan for what parts of the textbook 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 Homework
Monday, August 28 Chapter 1
Calculus
Course intro, section 1.1
Wednesday, August 30 Section 1.2: geometry of Rⁿ
Friday, September 1 Section 1.2: critical points for Rⁿ
Monday, September 4 Labor Day: no class
Wednesday, September 6 Section 1.3: Sylvester's criterion (Theorem 1.3.3)
Friday, September 8 Section 1.5: Eigenvalues HW 1 due
Monday, September 11 Section 1.4: Coercive functions, global optima
Wednesday, September 13 Chapter 2
Convexity
Section 2.1: Convex sets
Friday, September 15 Section 2.3: Convex functions, Jensen's inequality HW 2 due
Monday, September 18 Section 2.3: Building convex functions
Wednesday, September 20 Exam 1 (Topics that will be covered)
Friday, September 22 Section 2.4: The AM-GM inequality
Monday, September 25 Section 2.5: Geometric programming, duality
Wednesday, September 27 Section 2.5: Solving the dual geometric program
Friday, September 29 Overview of linear programming HW 3 due
Monday, October 2 Chapter 4
Least Squares
Section 4.1: Interpolation, best-fit lines
Wednesday, October 4 Section 4.2: Least squares fit, projections
Friday, October 6 Section 4.1: The Gram-Schmidt process HW 4 due
Monday, October 9 Section 4.3: Minimum norm solutions
Wednesday, October 11 Section 4.4: Generalized inner products
Friday, October 13 Chapter 5
Convex Programming
The KKT Conditions
Section 5.1: The closest point to a set HW 5 due
Monday, October 16 Section 5.1: The basic separation theorem
Wednesday, October 18 Exam 2 (Topics that will be covered)
Friday, October 20 Section 5.1: The support theorem
Monday, October 23 Lagrange multipliers
Wednesday, October 25 Section 5.2: Convex programs
Friday, October 27 Section 5.2: The KKT theorem HW 6 due
Monday, October 30 Section 5.2: KKT, Gradient form
Wednesday, November 1 Section 5.4: KKT duality
Friday, November 3 Section 5.3: Constrained GP example HW 7 due
Monday, November 6 Section 5.3: Constrained GP, general case
Wednesday, November 8 Chapter 6
Penalty Methods
Section 6.1: Penalty functions
Friday, November 10 Section 6.2: The penalty method HW 8 due
Monday, November 13 Examples with the penalty method
Wednesday, November 15 Exam 3 (Topics that will be covered)
Friday, November 17 Section 6.3: KKT via the penalty method
Monday, November 20Thanksgiving: no class
Wednesday, November 22
Friday, November 24
Monday, November 27 Chapter 3
Iterative methods
Wednesday, November 29
Friday, December 1 HW 9 due
Monday, December 4
Wednesday, December 6 Other topics
Friday, December 8 HW 10 due
Monday, December 11
Wednesday, December 13
Friday, December 15 Final Exam 8:00-11:00am in 241 Altgeld Hall

Last updated November 10, 2017. Mikhail Lavrov <mlavrov@illinois.edu>