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arXiv · 2510.22715

The Iterates of Nesterov's Accelerated Algorithm Converge in The Critical Regimes

Radu Ioan Bot·Jalal Fadili·Dang-Khoa Nguyen
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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 $L$-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.

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Radu Ioan Bot, Jalal Fadili, Dang-Khoa Nguyen. 2025-10-26. The Iterates of Nesterov's Accelerated Algorithm Converge in The Critical Regimes. https://arxiv.org/abs/2510.22715

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