Math 484: Nonlinear Programming (Fall 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

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 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.

Exams

There will be three evening midterm exams: Wednesday 9/19, Wednesday 10/17, and Wednesday 11/14 from 7pm to 8:30pm in 241 Altgeld Hall. Correspondingly, three lectures will be canceled, though not necessarily on the same day as the exam; I'll announce the canceled lectures and update the syllabus below well in advance.

The final exam will be held Wednesday 12/19 from 7pm to 10pm in 441 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
Mon Aug 27 Chapter 1
Calculus
Section 1.1: 1-dimensional optimization
Wed Aug 29 Section 1.2: Geometry of ℝn
Fri Aug 31 Section 1.2: Critical points in ℝn
Mon Sep 3 Labor Day: no class
Wed Sep 5 Section 1.3: Sylvester's criterion
Fri Sep 7 Section 1.5: Eigenvalues HW 1 due
Mon Sep 10 Section 1.4: Closed and bounded sets
Wed Sep 12 Chapter 2
Convexity
Section 2.1: Convex sets
Fri Sep 14 Section 2.3: Convex functions HW 2 due
Mon Sep 17 Section 2.3: Building convex functions
Wed Sep 19 Section 2.4: The AM-GM inequality Exam: 7pm in 241 AH (Topics)
Fri Sep 21 Section 2.5: Geometric programming
Mon Sep 24 Section 2.5: Solving the dual GP
Wed Sep 26 Section 2.3: Derivatives of convex functions HW 3 due
Fri Sep 28 No class
Mon Oct 1Chapter 4
Least Squares
Section 4.1: Interpolation and best-fit lines
Wed Oct 3 Section 4.2: Least-squares fit and projections
Fri Oct 5 Section 4.1: The Gram–Schmidt process HW 4 due
Mon Oct 8 Section 4.3: Minimum norm solutions
Wed Oct 10 Section 4.4: Generalized inner products
Fri Oct 12 Chapter 5
Convex Programming
The KKT Theorem
The method of Lagrange multipliers HW 5 due
Mon Oct 15 Section 5.1: The obtuse angle criterion
Wed Oct 17 Section 5.1: Separation and support theorems Exam: 7pm in 241 AH (Topics)
Fri Oct 19 Section 5.1: Applications
Mon Oct 22 Section 5.2: Convex programs
Wed Oct 24 Section 5.2: The KKT theorem HW 6 due
Fri Oct 26 No class
Mon Oct 29 Section 5.2: KKT theorem, gradient form
Wed Oct 31 Section 5.4: KKT duality
Fri Nov 2 Section 5.3: Deriving the KKT dual HW 7 due
Mon Nov 5 Section 5.3: Constrained geometric programs
Wed Nov 7 Chapter 6
Penalty Methods
Section 6.1: Intro to penalty methods
Fri Nov 9 Section 6.2: Guaranteeing optimality HW 8 due
Mon Nov 12 Section 6.2: More on coercive functions
Wed Nov 14 Section 6.3: KKT and the penalty method Exam: 7pm in 241 AH (Topics)
Fri Nov 16 Dealing with equality constraints
Mon Nov 19Fall break: no class
Wed Nov 21
Fri Nov 23
Mon Nov 26Chapter 3
Iterative Methods
Section 3.1: Newton's method
Wed Nov 28 No class
Fri Nov 30 Section 3.1: Newton's method for minimization HW 9 due
Mon Dec 3 Section 3.2: Steepest descent
Wed Dec 5 Section 3.3: General descent methods
Fri Dec 7 Section 3.3: Using descent methods
Mon Dec 10 Section 3.4: Broyden's method HW 10 due
Wed Dec 12 Review for final exam
Wed Dec 19 Final Exam from 7pm to 10pm in Altgeld 441 (Topics)

Last updated December 12, 2018. Mikhail Lavrov <mlavrov@illinois.edu>