  There has been significant interest in generalizations of the Nesterov
accelerated gradient descent algorithm due to its improved performance
guarantee compared to the standard gradient descent algorithm, and its
applicability to large scale optimization problems arising in deep learning. A
particularly fruitful approach is based on numerical discretizations of
differential equations that describe the continuous time limit of the Nesterov
algorithm, and a generalization involving time-dependent Bregman Lagrangian and
Hamiltonian dynamics that converges at an arbitrarily fast rate to the minimum.
We develop a Lie group variational discretization based on an extended path
space formulation of the Bregman Lagrangian on Lie groups, and analyze its
computational properties with two examples in attitude determination and
vision-based localization.
