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.
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.
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).
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.
|Wed January 17||Chapter 1
|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
|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
|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
|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 19||Spring break: no class|
|Wed March 21|
|Fri March 23|
|Mon March 26||Chapter 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
|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)|