Momentum-based gradient descent methods for Lie groups
<|reference_start|>Momentum-based gradient descent methods for Lie groups: 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.<|reference_end|>
@article{campos2024momentum-based,
    title={Momentum-based gradient descent methods for Lie groups},
    author={C'edric M. Campos, David Mart'in de Diego, Jos'e Torrente},
    journal={arXiv preprint arXiv:2404.09363},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.09363},
    primaryClass={math.OC cs.LG cs.NA math.DG math.NA}
}