73 citations · 670 across the 56 of their papers we have counts for
6 papers · 1 filter
Momentum-based gradient descent methods for Lie groups
Cédric M. Campos, David Martín de Diego, José Torrente-Teruel
Polyak's Heavy Ball (PHB; Polyak, 1964), a.k.a. Classical Momentum, and Nesterov's Accelerated Gradient (NAG; Nesterov, 1983) are well-established momentum-descent methods for opti…
Higher-order retraction maps and construction of numerical methods for optimal control of mechanical systems
Alexandre Anahory Simoes, Maria Barbero Liñán, Leonardo Colombo +1
Retractions maps are used to define a discretization of the tangent bundle of the configuration manifold as two copies of the configuration manifold where the dynamics take place.…
A parallel iterative method for variational integration
Sebastián J. Ferraro, David Martín de Diego, Rodrigo Takuro Sato Martín de Almagro
Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solutio…
A Discrete Variational Derivation of Accelerated Methods in Optimization
Cédric M. Campos, Alejandro Mahillo, David Martín de Diego
Many of the new developments in machine learning are connected with gradient-based optimization methods. Recently, these methods have been studied using a variational perspective.…
A geometric approach to the optimal control of nonholnomic mechanical systems
Anthony Bloch, Leonardo Colombo, Rohit Gupta +1
In this paper, we describe a constrained Lagrangian and Hamiltonian formalism for the optimal control of nonholonomic mechanical systems. In particular, we aim to minimize a cost f…
Discrete variational integrators and optimal control theory
M. de Leon, D. Martin de Diego, A. Santamaria-Merino
A geometric derivation of numerical integrators for optimal control problems is proposed. It is based in the classical technique of generating functions adapted to the special feat…