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arXiv:2510.23513math.OC

Point Convergence of Nesterov's Accelerated Gradient Method: An AI-Assisted Proof

Uijeong Jang, Ernest K. Ryu

Abstract

The Nesterov accelerated gradient method, introduced in 1983, has been a cornerstone of optimization theory and practice. Yet the question of its point convergence had remained open. In this work, we resolve this longstanding open problem in the affirmative. The discovery of the proof was heavily assisted by ChatGPT, a proprietary large language model, and we describe the process through which its assistance was elicited.

arXiv comments
17 pages
Journal reference
DOI
Subjects
math.OCOptimization and Control

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Linked by 2 identifiable commenters in 2 comments across 2 threads, from Nov 2025 to May 2026.

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  1. Agentic Coding Is a Trap 1 comment

    • You're right, definitely as a helper, not a one shot thing. Here's an example unrelated to the Erdos problems: https://arxiv.org/abs/2510.23513

      helloplanetsView on HNParent context

  2. GPT-5 helped mathematician Ernest Ryu solve a 40-year-old open problem 1 comment

    • Direct link, https://arxiv.org/abs/2510.23513 > "The Nesterov accelerated gradient method, introduced in 1983, has been a cornerstone of optimization theory and practice. Yet the question of its point convergence had remained open. In this work, we resolve this longstanding open…

      perihelionsView on HNParent context

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