The Institute for Robotics and Intelligent Machines presents “Accelerated Optimization in the PDE Framework” by Anthony J. Yezzi of Georgia Tech. The event will be held in the Marcus Nanotechnology Building, Rooms 1116-1118, from 12:15-1:15 p.m. and is open to the public.
Following the seminal work of Nesterov, accelerated optimization methods (sometimes referred to as momentum methods) have been used to powerfully boost the performance of first-order, gradient-based parameter estimation in scenarios where second-order optimization strategies are either inapplicable or impractical. Not only does accelerated gradient descent converge considerably faster than traditional gradient descent, but it performs a more robust local search of the parameter space by initially overshooting and then oscillating back as it settles into a final configuration, thereby selecting only local minimizers with an attraction basin large enough to accommodate the initial overshoot. This behavior has made accelerated search methods particularly popular within the machine learning community where stochastic variants have been proposed as well. So far, however, accelerated optimization methods have been applied to searches over finite parameter spaces. We show how a variational setting for these finite dimensional methods (recently formulated by Wibisono, Wilson, and Jordan) can be extended to the infinite dimensional setting, both in linear functional spaces as well as to the more complicated manifold of 2D curves and 3D surfaces. Moreover, we also show how extremely simple explicit discretization schemes can be used to efficiently solve the resulting class of high-dimensional optimization problems.
Anthony J. Yezzi was born in Gainesville, Florida and grew up in Minneapolis, Minnesota. He obtained both his Bachelor's degree and his Ph.D. in the Department of Electrical Engineering at the University of Minnesota with minors in mathematics and music.
After completing his Ph.D., he continued his research as a post-doctoral research associate in the Laboratory for Information and Decision Systems at Massachusetts Institute of Technology in Boston.
His research interests fall broadly within the fields of image processing and computer vision. In particular, he is interested in curve and surface evolution theory and partial differential equation techniques as they apply to topics within these fields, such as segmentation, image smoothing, and enhancement, optical flow, stereo disparity, shape from shading, object recognition, and visual tracking. Much of Yezzi's work is tailored to problems in medical imaging, including cardiac ultrasound, MRI, and CT.
Yezzi joined the Georgia Tech faculty in the fall of 1999 where he has taught courses in digital signal processing and is working to develop advanced courses in computer vision and medical image processing. He consults with industry in the areas of visual inspection and medical imaging. His hobbies include classical guitar, opera, and martial arts.