# A class of generalized Nesterov's accelerated gradient method from dynamical perspective

arXiv: https://arxiv.org/abs/2508.12816 · HTML: https://mlsanity.com/paper/2508.12816/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Aug 2025.

## Built on by (most cited first, 1 of 1)

- [Enhanced NIRMAL Optimizer With Damped Nesterov Acceleration: A Comparative Analysis](https://mlsanity.com/paper/2508.16550/) (2025)

## Abstract (arXiv)

We propose a class of textitEuler-Lagrange equations indexed by a pair of parameters (α,r) that generalizes Nesterov's accelerated gradient methods for convex (α=1) and strongly convex (α=0) functions from a continuous-time perspective. This class of equations also serves as an interpolation between the two Nesterov's schemes. The corresponding textitHamiltonian systems can be integrated via the symplectic Euler scheme with a fixed step-size. Furthermore, we can obtain the convergence rates for these equations (0<α<1) that outperform Nesterov's when time is sufficiently large for μ-strongly convex functions, without requiring a priori knowledge of μ. We demonstrate this by constructing a class of Lyapunov functions that also provide a unified framework for Nesterov's schemes for convex and strongly convex functions.