Time-adaptive Lagrangian variational integrators for accelerated optimization

A variational framework for accelerated optimization was recently introduced on normed vector spaces and Riemannian manifolds in Wibisono et al. (2016) Duruisseaux Leok (2021). It observed that a careful combination of timeadaptivity symplecticity the numerical integration can result significant gain computational efficiency. is however well known symplectic integrators lose their near energy preservation properties when variable time-steps are used. The most common approach to circumvent this problem involves Poincare transformation Hamiltonian side, used (2021) construct efficient explicit algorithms optimization. However, current formulations do not make intrinsic sense more general such as Lie groups. In contrast, Lagrangian well-defined manifolds, so we develop here time-adaptivity use resulting geometric solve problems