Accelerated Optimization in the PDE Framework
Mar 16, 2018 | Atlanta, GA
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 were 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 a
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 framework for these finite dimensional methods (recently
formulated by Wibisono, Wilson, and Jordan) can be extended to the
infinite dimensional setting and, in particular, to the manifold of
planar curves in order to yield a new class of accelerated geometric,
PDE-based active contours.
Professor Yezzi 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 at the Laboratory for Information and Decision Systems at Massachusetts Institute of Technology in Boston, MA.
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.
Much of Dr. Yezzi's work is particularly tailored to problems in medical imaging, including cardiac ultrasound, MRI, and CT. He joined the Georgia Tech faculty in the fall of 1999 where he has taught courses in DSP and is working to develop advanced courses in computer vision and medical image processing.