MA 273C Advanced Techniques in Computational Mathematics - Optimization on Manifolds

Spring 2017

This course is relevant to engineers, scientists, and mathematicians with an interest in optimization problems involving manifolds. The application areas addressed will be tailored to the interests of the course participants.
WebReg incorrectly enforces MATH 273B as a prerequisite for this course, but the material in this class is self-contained. Please contact me with your PID if you need an override in order to register for this class.

Smooth optimization on manifolds naturally generalizes smooth optimization in Euclidean spaces in a manner that is of interest in a variety of applications, including modal analysis, blind source separation (via independent component analysis), pose estimation in computer vision, and model reduction in dynamical systems. Manifolds of interest include the Stiefel manifolds and Grassmann manifolds.
After presenting a number of motivating applications, we will introduce the basics of differential manifolds and Riemannian geometry, and describe how methods in optimization, like line-search, Newton's method, and trust region methods can be generalized to the case of manifolds. The course will assume only a basic knowledge of matrix algebra and real analysis.

The resources below are password protected with the user name ma273c, and the password is the first 4 digits of:
$\sqrt{6\sum_{n=1}^\infty}{1}{n^2}}$ .

Your grade in the course is based on your project and your 20-minute project presentation during the last week of classes.
The topic of your project should be decided in consultation with the instructor before the end of the first month of class.