A Variational Formulation of Accelerated Optimization on Riemannian Manifolds

DOI10.1137/21M1395648zbMath1504.37104arXiv2101.06552OpenAlexW3124961975WikidataQ115246868 ScholiaQ115246868MaRDI QIDQ5863993

Valentin Duruisseaux, Melvin Leok

Publication date: 3 June 2022

Published in: SIAM Journal on Mathematics of Data Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.06552

zbMATH Keywords

Riemannian optimizationaccelerated optimizationsymplectic optimizationNesterov accelerated gradient

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) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15)

Related Items (6)

Accelerated optimization on Riemannian manifolds via discrete constrained variational integrators ⋮ Practical perspectives on symplectic accelerated optimization ⋮ Fast gradient method for low-rank matrix estimation ⋮ Time-adaptive Lagrangian variational integrators for accelerated optimization ⋮ Bregman dynamics, contact transformations and convex optimization ⋮ High-order symplectic Lie group methods on \(SO(n)\) using the polar decomposition

Cites Work

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• Variational and geometric structures of discrete Dirac mechanics
• Accelerating the cubic regularization of Newton's method on convex problems
• Introductory lectures on convex optimization. A basic course.
• Accelerated optimization on Riemannian manifolds via discrete constrained variational integrators
• A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights
• Discrete mechanics and variational integrators
• Introduction to Riemannian Manifolds
• A variational perspective on accelerated methods in optimization
• Adaptive Hamiltonian Variational Integrators and Applications to Symplectic Accelerated Optimization
• Geometric Numerical Integration
• Riemannian geometry and geometric analysis

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