Georgia Institute of Technology Institute for Robotics and Intelligent Machines

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.