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 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).
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 ℝ^{n} | ||
Fri Aug 31 | Section 1.2: Critical points in ℝ^{n} | ||
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 1 | Chapter 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 19 | Fall break: no class | ||
Wed Nov 21 | |||
Fri Nov 23 | |||
Mon Nov 26 | Chapter 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) |