mlsanityData to 14 Oct 2026

A Continuous-time Perspective for Modeling Acceleration in Riemannian Optimization

arXiv 1910.10782 ↗First posted 23 Oct 2019math.OCcited by 25

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Abstract (arXiv)

We propose a novel second-order ODE as the continuous-time limit of a Riemannian accelerated gradient-based method on a manifold with curvature bounded from below. This ODE can be seen as a generalization of the ODE derived for Euclidean spaces, and can also serve as an analysis tool. We study the convergence behavior of this ODE for different classes of functions, such as geodesically convex, strongly-convex and weakly-quasi-convex. We demonstrate how such an ODE can be discretized using a semi-implicit and Nesterov-inspired numerical integrator, that empirically yields stable algorithms which are faithful to the continuous-time analysis and exhibit accelerated convergence.

Key facts. Cited by 25 papers in the map (data through 14 Oct 2026). First posted on arXiv 23 Oct 2019.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 2; 2022: 8; 2023: 4; 2024: 6; 2025: 4; 2026: 1.

25 papers.

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  1. 2021On Riemannian Stochastic Approximation Schemes with Fixed Step-Sizecited by 12
  2. 2022Differentially private Riemannian optimizationcited by 12
  3. 2022First-Order Algorithms for Min-Max Optimization in Geodesic Metric Spacescited by 10
  4. 2023Simplifying Momentum-based Positive-definite Submanifold Optimization with Applications to Deep Learningcited by 10
  5. 2022Sion's Minimax Theorem in Geodesic Metric Spaces and a Riemannian Extragradient Algorithmcited by 9
  6. 2021Revisiting the Role of Euler Numerical Integration on Acceleration and Stability in Convex Optimizationcited by 6
  7. 2022Shape And Structure Preserving Differential Privacycited by 6
  8. 2023Minimizing Dynamic Regret on Geodesic Metric Spacescited by 6
  9. 2022Riemannian accelerated gradient methods via extrapolationcited by 5
  10. 2024Federated Learning on Riemannian Manifolds with Differential Privacycited by 5
  11. 2024Projected Neural Differential Equations for Learning Constrained Dynamicscited by 5
  12. 2022Accelerated Riemannian Optimization: Handling Constraints with a Prox to Bound Geometric Penaltiescited by 4
13 more
  1. 2023Riemannian Projection-free Online Learningcited by 4
  2. 2025Decentralized Online Riemannian Optimization Beyond Hadamard Manifoldscited by 4
  3. 2024A Framework for Bilevel Optimization on Riemannian Manifoldscited by 3
  4. 2025Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectivescited by 3
  5. 2025Efficient Bayesian Computation Using Plug-and-Play Priors for Poisson Inverse Problemscited by 2
  6. 2025Accelerated Markov Chain Monte Carlo Algorithms on Discrete Statescited by 2
  7. 2022Riemannian Stochastic Gradient Method for Nested Composition Optimizationcited by 1
  8. 2022Rieoptax: Riemannian Optimization in JAXcited by 1
  9. 2023Extragradient Type Methods for Riemannian Variational Inequality Problemscited by 1
  10. 2024Quantitative Convergences of Lie Group Momentum Optimizerscited by 1
  11. 2024Learning-Rate-Free Stochastic Optimization over Riemannian Manifoldscited by 1
  12. 2026Decentralized Online Riemannian Optimization for Strongly Geodesically Convex Functionscited by 1
  13. 2024Generalized Continuous-Time Models for Nesterov's Accelerated Gradient Methodscited by 0