mlsanityData to 14 Oct 2026

Near-optimal Closed-loop Method via Lyapunov Damping for Convex Optimization

arXiv 2311.10053 ↗First posted 16 Nov 2023math.OC cs.LG math.DScited by 1

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Abstract (arXiv)

We introduce an autonomous system with closed-loop damping for first-order convex optimization. While, to this day, optimal rates of convergence are almost exclusively achieved by non-autonomous methods via open-loop damping (e.g., Nesterov's algorithm), we show that our system, featuring a closed-loop damping, exhibits a rate arbitrarily close to the optimal one. We do so by coupling the damping and the speed of convergence of the system via a well-chosen Lyapunov function. By discretizing our system we then derive an algorithm and present numerical experiments supporting our theoretical findings.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 14 of its 40 references that are in the map. First posted on arXiv 16 Nov 2023.

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14 of 40 references.

References · 14

  1. 2015A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insightscited by 206
  2. 2016A Variational Perspective on Accelerated Methods in Optimizationcited by 110
  3. 2018Understanding the Acceleration Phenomenon via High-Resolution Differential Equationscited by 69
  4. 2019First-order optimization algorithms via inertial systems with Hessian driven dampingcited by 22
  5. 2016Fast convex optimization via inertial dynamics with Hessian driven dampingcited by 13
  6. 2017Rate of convergence of the Nesterov accelerated gradient method in the subcritical case α ≤ 3cited by 9
  7. 2022From the Ravine method to the Nesterov method and vice versa: a dynamical system perspectivecited by 9
  8. 2018Optimal convergence rates for Nesterov accelerationcited by 8
  9. 2019An extension of the second order dynamical system that models Nesterov's convex gradient methodcited by 5
  10. 2019A Control-Theoretic Perspective on Optimal High-Order Optimizationcited by 5
  11. 2020Fast optimization via inertial dynamics with closed-loop dampingcited by 4
  12. 2015A dynamic approach to a proximal-Newton method for monotone inclusions in Hilbert spaces, with complexity O(1/n^2)cited by 2
2 more
  1. 2023Fast convex optimization via closed-loop time scaling of gradient dynamicscited by 2
  2. 2015Asymptotic for a second order evolution equation with convex potential and vanishing damping termcited by 1

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  1. 2025Stochastic Adaptive Gradient Descent Without Descentcited by 0