Time-adaptive Lagrangian variational integrators for accelerated optimization on manifolds

V Duruisseaux, M Leok - arXiv preprint arXiv:2201.03774, 2022 - arxiv.org
A variational framework for accelerated optimization was recently introduced on normed
vector spaces and Riemannian manifolds in Wibisono et al.(2016) and Duruisseaux and …

Variational unscented Kalman filter on matrix Lie groups

T Li, J Wang - Automatica, 2025 - Elsevier
In this paper, several estimation algorithms called the variational unscented Kalman filters
(UKF-Vs) are proposed for matrix Lie groups. The proposed filters are inspired by the …

The application of Goeken–Johnson's Runge–Kutta methods in unconstrained convex optimization

G Krivovichev - Numerical Algorithms, 2024 - Springer
The paper is devoted to the construction and analysis of gradient methods for convex
optimization based on the explicit Goeken–Johnson's Runge–Kutta methods for solving the …

Variational Principles for Hamiltonian Systems

BK Tran, M Leok - arXiv preprint arXiv:2410.02960, 2024 - arxiv.org
Motivated by recent developments in Hamiltonian variational principles, Hamiltonian
variational integrators, and their applications such as to optimization and control, we present …

Momentum-based gradient descent methods for Lie groups

CM Campos, DM de Diego, J Torrente - arXiv preprint arXiv:2404.09363, 2024 - arxiv.org
Polyak's Heavy Ball (PHB; Polyak, 1964), aka Classical Momentum, and Nesterov's
Accelerated Gradient (NAG; Nesterov, 1983) are well know examples of momentum-descent …

[图书][B] Symplectic Numerical Integration at the Service of Accelerated Optimization and Structure-Preserving Dynamics Learning

V Duruisseaux - 2023 - search.proquest.com
Symplectic numerical integrators for Hamiltonian systems form the paramount class of
geometric numerical integrators, and have been very well investigated in the past forty …

[PDF][PDF] Gradient descent methods based on the Runge—Kutta method with Lagrange—Buhrman decomposition

KR Borisovic - 2024 - dspace.spbu.ru
The graduate work is devoted to the development and analysis of new numerical
optimization methods based on the Runge—Kutta method with Lagrange—Burmann …