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 …
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 …
(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 …
optimization based on the explicit Goeken–Johnson's Runge–Kutta methods for solving the …
Variational Principles for Hamiltonian Systems
Motivated by recent developments in Hamiltonian variational principles, Hamiltonian
variational integrators, and their applications such as to optimization and control, we present …
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 …
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 …
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 …
optimization methods based on the Runge—Kutta method with Lagrange—Burmann …