Math 484: Nonlinear Programming (Spring 2018)

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:

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

I might adjust this scale slightly - don't consider it set in stone until after the first midterm. But that's the basic idea.

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 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 evening midterm exams: Wednesday 2/7 and Wednesday 3/7 from 7pm to 8:30pm in 341 Altgeld Hall, and Wednesday 4/18 from 7pm to 8:30pm in Talbot 103. Correspondingly, three lectures will be canceled, not necessarily in the same week as the midterm exams; these are also marked in the syllabus below.

The final exam will be given on Wednesday, May 9, 7:00-10:00pm, in 345 Altgeld Hall (our usual classroom).

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/Exams
Wed January 17 Chapter 1
Calculus
Section 1.1: 1D Optimization
Fri January 19 Section 1.2: Geometry of Rn
Mon January 22 Section 1.2: Critical points in Rn
Wed January 24 Section 1.3: Sylvester's criterion
Fri January 26 Section 1.4: Eigenvalues HW 1 due
Mon January 29 Section 1.5: Compactness
Wed January 31 Chapter 2
Convexity
Section 2.1: Convex sets
Fri February 2 Section 2.3: Convex functions HW 2 due
Mon February 5 Section 2.3: Building convex functions
Wed February 7 Section 2.4: The AM-GM inequality Exam: 7pm in 341 AH (Topics)
Fri February 9 Section 2.5: Geometric programming
Mon February 12 Section 2.5: Solving the dual GP
Wed February 14 Affine transformations HW 3 due
Fri February 16 No class
Mon February 19 Chapter 3
Iterative Methods
Section 3.1: Introduction to Newton's method
Wed February 21 Section 3.1: Minimizing with Newton's method
Fri February 23 Section 3.2: Method of steepest descent HW 4 due
Mon February 26 Section 3.3: Criteria for descent methods
Wed February 28 Section 3.3: Choosing descent directions
Fri March 2 Section 3.4: Broyden's method HW 5 due
Mon March 5 Finding eigenvalues
Wed March 7 Chapter 4
Least Squares
Section 4.2: Least squares fit Exam: 7pm in 341 AH (Topics)
Fri March 9 Section 4.1: The Gram-Schmidt Process
Mon March 12 Section 4.3: Minimum-norm solutions
Wed March 14 Section 4.4: Generalized inner products HW 6 due
Fri March 16 No class
Mon March 19Spring break: no class
Wed March 21
Fri March 23
Mon March 26Chapter 5
The KKT Theorem
Section 5.1: More about sets
Wed March 28 Section 5.1: The obtuse angle criterion
Fri March 30 Section 5.1: The support theorem HW 7 due
Mon April 2 Section 5.1: The support theorem
Wed April 4 Section 5.1: Sensitivity vectors
Fri April 6 Section 5.2: The KKT Theorem HW 8 due
Mon April 9 Section 5.2: KKT, Gradient form
Wed April 11 Section 5.4: KKT duality Exam: 7pm in Talbot 103 (Topics)
Fri April 13 No class
Mon April 16 Section 5.3/5.4: GP duality via KKT
Wed April 18 Section 5.3/5.4: Constrained GP duality
Fri April 20 Section 5.3: Finding the GP dual HW 9 due
Mon April 23 Chapter 6
Penalty Methods
Section 6.1: Intro to penalty methods
Wed April 25 Section 6.2: Theorem 6.2.3
Fri April 27 Section 6.2: Corollary 6.2.4, coercive functions HW 10 due
Mon April 30 Equality constraints in KKT
Wed May 2 Section 6.3: The penalty method and KKT duality
Wed May 9 Final Exam 7:00-10:00pm in 345 Altgeld Hall (Topics)

Last updated May 3, 2018. Mikhail Lavrov <mlavrov@illinois.edu>