NONLINEAR OPTIMIZATION

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:

Homeworks: There will be weekly homework assignments, worth in total 35 percent of your grade.

Midterms: There will be one midterm (Friday, May 3rd, 2019). The content of the midterm will be discussed in advance. The midterm is worth 30 percent of your grade.

Final Exam: There will be a final exam on June 12, 2019 at 8:30-10:20 in ECE 105. The final exam is comprehensive and is worth 35 percent of your grade.

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.