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.

翻译：波利亚克重球法（PHB；Polyak, 1964），亦称经典动量法，以及涅斯捷罗夫加速梯度法（NAG；Nesterov, 1983），是优化领域中众所周知的动量下降方法实例。尽管后者性能优于前者，但文献中仅描述了类PHB方法在非线性空间中的推广。本文基于经典动量法与加速动量法之间变分的一一对应关系（Campos等人，2023），提出了一种适用于李群优化的类NAG方法推广。文中给出了数值实验。