Adaptive Hamiltonian Variational Integrators and Applications to Symplectic Accelerated Optimization

DOI10.1137/20M1383835zbMath1483.37099arXiv1709.01975OpenAlexW3194431487MaRDI QIDQ5010240

Valentin Duruisseaux, Jeremy Schmitt, Melvin Leok

Publication date: 25 August 2021

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.01975

zbMATH Keywords

symplectic integratorsvariational integratorstime adaptivityaccelerated optimization

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Dynamical systems in optimization and economics (37N40) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15)

Related Items (9)

Multisymplectic Hamiltonian variational integrators ⋮ Accelerated optimization on Riemannian manifolds via discrete constrained variational integrators ⋮ Performance assessment of energy-preserving, adaptive time-step variational integrators ⋮ Practical perspectives on symplectic accelerated optimization ⋮ Time-adaptive Lagrangian variational integrators for accelerated optimization ⋮ A Herglotz-based integrator for nonholonomic mechanical systems ⋮ Bregman dynamics, contact transformations and convex optimization ⋮ High-order symplectic Lie group methods on \(SO(n)\) using the polar decomposition ⋮ A Variational Formulation of Accelerated Optimization on Riemannian Manifolds

Uses Software

• Taylor
• ADiGator
• AdaGrad
• RMSprop
• Adam

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