The Iterates of Nesterov's Accelerated Algorithm Converge in The Critical Regimes
Optimization and Control
2025-11-03 v2
Abstract
In this paper, we prove that the iterates of the accelerated Nesterov's algorithm in the critical regime do converge in the weak topology to a global minimizer of an -smooth function in a real Hilbert space, hence answering positively a conjecture posed by H. Attouch and co-authors a decade ago. This result is the algorithmic case of a very recent result on the continuous-time system posted by E. Ryu on X, with assistance from ChatGPT.
Cite
@article{arxiv.2510.22715,
title = {The Iterates of Nesterov's Accelerated Algorithm Converge in The Critical Regimes},
author = {Radu Ioan Bot and Jalal Fadili and Dang-Khoa Nguyen},
journal= {arXiv preprint arXiv:2510.22715},
year = {2025}
}