NONLINEAR OPTIMIZATION
Instructor: Dmitriy Drusvyatskiy E-Mail: ddrusv(at)math(dot)washington(dot)edu
Phone: 543-9435 Hours: Wednesdays 1:00-3:00 PM
Office: PDL C-434
TA: Scott Roy E-Mail: scottroy(at)math(dot)washington(dot)edu
Office: PDL C-8D Hours: Thursday 3:30-5:30
Prerequisites: Math (308) & (327 or 334) Classroom: MUE 155 Lecture time: MWF 10:30 AM


URL for the course website:

Course Content:

A mathematical optimization problem is one in which a given function is either minimized or maximized relative to some set or range of choices available in a given situation. Optimization problems arise in a multitude of ways as a means of solving problems in engineering design, portfolio design, system management, parameter estimation, statistics, maching learning, and in the modeling of physical and behavioral phenomena. Math 408 is an introductory course in numerical methods for continuous optimization in finite dimensions. This field of study is often refered to as mathematical programming, and within this field we will focus on nonlinear programming.

Background and Prerequisites:

This course requires a background in multi-variable calculus. In order to succeed you will need to be conversant with the differential properties of smooth vector valued mappings. In particular, you will need to know properties of the gradient and Hessian. Moreover, some background in linear algebra is also required. In particular, you will need to know some results concerning the eigenvalue decomposition of a symmetric matrix, Gaussian elimination (LU factorization), and Gram--Schmidt orthogonalization (QR factorization). However, I do not expect everyone to have the the same level of preparation. Consequently, all of the material discussed above will be reviewed with most proofs omitted.

Grading:

Quizzes: There are 8 fifteen minute quizzes. The quizzes are given each Friday, except for the Friday of the week when the midterm is given and the last Friday of the quarter. The quizzes cover the homework of the previous week. The potential content of the quiz will be announced the Wednesday before the quiz. Each quiz is worth 70 points. Your top 5 quiz scores count toward your grade.

Midterms: There is one midterm: date Friday, February 12th. The content of the midterm will be discussed in advance and a sample midterm will be distributed before the exam. The midterm is worth 300 points.

Final Exam: There will be a final exam on Monday, March 14, 2016, at 8:30-10:20 am. The final exam is comprehensive. A sample final exam will be distributed. The final exam is worth 350 points.

Final Grade: The total number of possible points is 1000: 350 quiz pts + 300 midterm pts + 350 final exam pts = 1000 points.
Your final grade will be based on these points. One class curve is computed after the final exam has been scored.

Time Conflicts with an Exam:

There will be no make-up quizzes or exams except in the case of a documented emergency. In the event of an unavoidable conflict with a midterm (an athletic meet, wedding, funeral, etc...), you must notify me as soon as you are aware of the conflict (a minimum of 1 week prior to the exam date) so that we can arrange for you to take the exam BEFORE the actual exam date. In the event of an unavoidable conflict with the final exam, you will need to submit a written petition for this purpose to me as soon as you are aware of the conflict.

Incomplete:

A grade of Incomplete will be given only if a student is doing satisfactory work up until the end of the quarter, and then misses the final exam due to a documented medical or family emergency.

Important Dates:

Holidays: Jan. 18, Feb. 15

Quiz Dates: Jan. 8, 15, 22, 29; Feb. 5, 19, 26; Mar. 4

Last Day of Class: Friday, March 11.

Midterm Date: Friday, February 12th

Final Exam: Monday, March 14, 2016, at 8:30-10:20 am