Momentum-based gradient descent methods for Lie groups
Cédric M. Campos David Martín de Diego José Torrente
Polyak's Heavy Ball (PHB; Polyak, 1964), a.k.a. Classical Momentum, and
Nesterov's Accelerated Gradient (NAG; Nesterov, 1983) are well know examples of
momentum-descent methods for optimization. While the latter outperforms the
former, solely generalizations of PHB-like methods to nonlinear spaces have
been described in the literature. We propose here a generalization of NAG-like
methods for Lie group optimization based on the variational one-to-one
correspondence between classical and accelerated momentum methods (Campos et
al., 2023). Numerical experiments are shown.