This is an archived version of a class I taught at the University of Illinois Urbana-Champaign. For a while after I left, it remained on UIUC's website, but it was taken down when some subdomains got shuffled around. I think these are pretty okay lecture notes, and I know some people found them useful later, so I've decided to archive them on my personal webpage. If you spot any mistakes, please let me know.
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 2/6, Wednesday 3/6, and Wednesday 4/10 from 7pm to 8:30pm in 241 Altgeld Hall. Correspondingly, three lectures will be canceled, not necessarily in the same week as the midterm exams. The first of these is already marked in the syllabus below.
The final exam will be Thursday 5/9 from 7pm to 10pm in 347 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.
|Mon January 14||Chapter 1
|Section 1.1: 1D Optimization|
|Wed January 16||Section 1.2: Geometry of ℝn|
|Fri January 18||No class|
|Mon January 21||MLK Day: no class|
|Wed January 23||Section 1.2: Critical points in ℝn|
|Fri January 25||Section 1.3, 1.5: Positive definite matrices||HW 1 due|
|Mon January 28||Section 1.3: Sylvester's criterion|
|Wed January 30||"Local minimizer" day: no class|
|Fri February 1||Section 1.4: Closed and bounded sets|
|Mon February 4||Chapter 2
|Section 2.1: Convex sets||HW 2 due|
|Wed February 6||Section 2.3: Convex functions||Exam: 7pm in 241 AH (Topics)|
|Fri February 8||Section 2.3: Building convex functions|
|Mon February 11||Section 2.3: Jensen's inequality|
|Wed February 13||Section 2.4: AM-GM inequality|
|Fri February 15||Section 2.5: Geometric programming||HW 3 due|
|Mon February 18||Section 2.5: Solving the dual GP|
|Wed February 20||Chapter 4
|Section 4.1: Interpolation and best-fit lines|
|Fri February 22||Section 4.2: Least-squares fit and projections||HW 4 due|
|Mon February 25||Section 4.1: Orthogonal matrices|
|Wed February 27||Section 4.3: Minimum-norm solutions|
|Fri March 1||Section 4.4: Generalized inner products||HW 5 due|
|Mon March 4||Chapter 5
The KKT Theorem
|Section 5.1: The obtuse angle criterion|
|Wed March 6||Section 5.1: The separation theorem||Exam: 7pm in 241 AH (Topics)|
|Fri March 8||No class|
|Mon March 11||Section 5.1: The support theorem; subgradients|
|Wed March 13||Section 5.2: Convex programming|
|Fri March 15||Section 5.2: The KKT theorem||HW 6 due|
|Mon March 18||Spring break: no class|
|Wed March 20|
|Fri March 22|
|Mon March 25||Chapter 5
|Section 5.2: KKT, gradient form|
|Wed March 27||Section 5.4: KKT duality|
|Fri March 29||Section 5.3: Finding dual constraints||HW 7 due|
|Mon April 1||Section 5.3: Geometric programming, again|
|Wed April 3||Chapter 6
|Section 6.1: Intro to penalty methods|
|Fri April 5||Section 6.2: Guaranteeing optimality||HW 8 due|
|Mon April 8||Section 6.2: More on coercive functions|
|Wed April 10||Section 6.3: KKT and the penalty method||Exam: 7pm in 241 AH (Topics)|
|Fri April 12||Equality constraints|
|Mon April 15||Chapter 3
|Section 3.1: Newton's method|
|Wed April 17||Section 3.1: Newton's method in ℝn|
|Fri April 19||Section 3.2: The steepest descent method||HW 9 due|
|Mon April 22||Section 3.3: More general descent methods|
|Wed April 24||Section 3.3: Using descent methods|
|Fri April 26||Section 3.4: Broyden's method|
|Mon April 29||Other stuff||KKT for local minimizers||HW 10 due|
|Wed May 1||Exam review (optional)|
|Thu May 9||Final Exam (Topics)|