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

Uijeong Jang; Ernest K. Ryu

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arXiv · 2510.23513

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

Uijeong Jang·Ernest K. Ryu

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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.

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Uijeong Jang, Ernest K. Ryu. 2025-10-27. Point Convergence of Nesterov's Accelerated Gradient Method: An AI-Assisted Proof. https://arxiv.org/abs/2510.23513

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