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

2025/10/27 by Uijeong Jang, Ernest K. Ryu, Jang, Uijeong +1 · 2 voices · 10 citations
#math.OC

paper · pdf · doi:10.48550/arxiv.2510.23513

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.

Citations

• Smooth minimization of non-smooth functions

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• Accelerated Proximal Gradient Methods in the affine-quadratic case: Strong convergence and limit identification
• Point Convergence Analysis of the Accelerated Gradient Method for Multiobjective Optimization: Continuous and Discrete
• Inertial Primal Dual Dynamics with Hessian-driven Damping for Saddle Point Problems
• The Iterates of Nesterov's Accelerated Algorithm Converge in The Critical Regimes
• Reinforced Generation of Combinatorial Structures: Hardness of Approximation
• Time Scaling Makes Accelerated Gradient Flow and Proximal Method Faster in Multiobjective Optimization

Discussions

• Another example of the increasingly common situation where AI helps an academic with intellectually challenging work (solving a 42-year-old open math problem). Seems like real value in combining exper [bsky, 76 points, 4 comments]
• OK, I'll accept your verdict for your field. I can only say in my field, there are now several papers, including one I wrote myself, where an LLM came up with novel insights. Here's just one example: [bsky, 0 points, 0 comments]

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