# An Adaptive and Parameter-Free Nesterov's Accelerated Gradient Method for Convex Optimization

arXiv: https://arxiv.org/abs/2505.11670 · HTML: https://mlsanity.com/paper/2505.11670/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 May 2025.

## Built on by (most cited first, 2 of 2)

- [Adaptive Delayed-Update Cyclic Algorithm for Variational Inequalities](https://mlsanity.com/paper/2603.29128/) (2026)
- [Stochastic Auto-conditioned Fast Gradient Methods with Optimal Rates](https://mlsanity.com/paper/2604.06525/) (2026)

## Abstract (arXiv)

We propose AdaNAG, an adaptive accelerated gradient method based on Nesterov's accelerated gradient method. AdaNAG is line-search-free, parameter-free, and achieves the accelerated convergence rates f(xk) - f_star = Oleft(1/k2right) and min_i∈left1,dots, kright |nabla f(xi)|2 = Oleft(1/k3right) for L-smooth convex function f. We provide a Lyapunov analysis for the convergence proof of AdaNAG, which additionally enables us to propose a novel adaptive gradient descent (GD) method, AdaGD. AdaGD achieves the non-ergodic convergence rate f(xk) - f_star = Oleft(1/kright), like the original GD. The analysis of AdaGD also motivated us to propose a generalized AdaNAG that includes practically useful variants of AdaNAG. Numerical results demonstrate that our methods outperform some other recent adaptive methods for representative applications.