- Lecture meets Mon/Wed/Fri 2:00-2:50pm in 241 Altgeld Hall.
- Office hours are Mon/Wed/Fri 3:00-4:00pm in 226 Illini Hall, or by appointment.
- Do not hesitate to contact me with questions via e-mail at mlavrov@illinois.edu.

The course grade will be calculated as follows, out of 660 points total:

- Homework: 160 points.
- Intermediate exams: 300 points.
- Final exam: 200 points.

You can check your grades via Moodle.

Your grade total will be converted to a letter grade according to the following scale:

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 at least 9 (most likely 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 in-class midterm exams (graded out of 100 points each) on the following dates:

- Wednesday, September 20,
- Wednesday, October 18,
- Wednesday, November 15.

The final exam will be given on Friday, December 15, 8:00-11:00am, in 241 Altgeld Hall.

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 |

Monday, August 28 | Chapter 1 Calculus |
Course intro, section 1.1 | |

Wednesday, August 30 | Section 1.2: geometry of Rⁿ | ||

Friday, September 1 | Section 1.2: critical points for Rⁿ | ||

Monday, September 4 | Labor Day: no class |
||

Wednesday, September 6 | Section 1.3: Sylvester's criterion (Theorem 1.3.3) | ||

Friday, September 8 | Section 1.5: Eigenvalues | HW 1 due | |

Monday, September 11 | Section 1.4: Coercive functions, global optima | ||

Wednesday, September 13 | Chapter 2 Convexity |
Section 2.1: Convex sets | |

Friday, September 15 | Section 2.3: Convex functions, Jensen's inequality | HW 2 due | |

Monday, September 18 | Section 2.3: Building convex functions | ||

Wednesday, September 20 | Exam 1 (Topics that will be covered) |
||

Friday, September 22 | Section 2.4: The AM-GM inequality | ||

Monday, September 25 | Section 2.5: Geometric programming, duality | ||

Wednesday, September 27 | Section 2.5: Solving the dual geometric program | ||

Friday, September 29 | Overview of linear programming | HW 3 due | |

Monday, October 2 | Chapter 4 Least Squares |
Section 4.1: Interpolation, best-fit lines | |

Wednesday, October 4 | Section 4.2: Least squares fit, projections | ||

Friday, October 6 | Section 4.1: The Gram-Schmidt process | HW 4 due | |

Monday, October 9 | Section 4.3: Minimum norm solutions | ||

Wednesday, October 11 | Section 4.4: Generalized inner products | ||

Friday, October 13 | Chapter 5 Convex Programming The KKT Conditions |
Section 5.1: The closest point to a set | HW 5 due |

Monday, October 16 | Section 5.1: The basic separation theorem | ||

Wednesday, October 18 | Exam 2 (Topics that will be covered) |
||

Friday, October 20 | Section 5.1: The support theorem | ||

Monday, October 23 | Lagrange multipliers | ||

Wednesday, October 25 | Section 5.2: Convex programs | ||

Friday, October 27 | Section 5.2: The KKT theorem | HW 6 due | |

Monday, October 30 | Section 5.2: KKT, Gradient form | ||

Wednesday, November 1 | Section 5.4: KKT duality | ||

Friday, November 3 | Section 5.3: Constrained GP example | HW 7 due | |

Monday, November 6 | Section 5.3: Constrained GP, general case | ||

Wednesday, November 8 | Chapter 6 Penalty Methods |
Section 6.1: Penalty functions | |

Friday, November 10 | Section 6.2: The penalty method | HW 8 due | |

Monday, November 13 | Examples with the penalty method | ||

Wednesday, November 15 | Exam 3 (Topics that will be covered) |
||

Friday, November 17 | Section 6.3: KKT via the penalty method | ||

Monday, November 20 | Thanksgiving: no class |
||

Wednesday, November 22 | |||

Friday, November 24 | |||

Monday, November 27 | Chapter 3 Iterative methods |
Section 3.1: Introduction to Newton's method | |

Wednesday, November 29 | Section 3.1: Minimizing with Newton's method | ||

Friday, December 1 | Section 3.2: Method of steepest descent | HW 9 due | |

Monday, December 4 | Section 3.3: Criteria for descent methods | ||

Wednesday, December 6 | Section 3.3: Choosing descent directions | ||

Friday, December 8 | Section 3.4: Broyden's method | HW 10 due | |

Monday, December 11 | Example of Broyden's method; eigenvalues | ||

Wednesday, December 13 | Review for the final exam | ||

Friday, December 15 | Final Exam 8:00-11:00am in 241 Altgeld Hall (Topics from Chapter 3, formula sheet) |

Last updated December 10, 2017. Mikhail Lavrov <mlavrov@illinois.edu>