Point Convergence of Nesterov's Accelerated Gradient Method
Statement
Nesterov's accelerated gradient method (1983) is a cornerstone of optimization, yet whether its iterates themselves converge to a minimizer, rather than just the function values, stayed open for over forty years. Jang and Ryu resolve it in the affirmative. Ryu first announced the continuous-time result on X; Bot, Fadili and Nguyen's concurrent human proof of the critical-regime case (answering a decade-old conjecture of Attouch and co-authors) explicitly credits that AI-assisted announcement as what it discretizes.
Record
Comments
No person has examined this. Nothing here has been checked at all. say whether it holds →
proof attempt · #1
Uijeong Jang and Ernest K. Ryu, using GPT-5 ProThat credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
The discovery was heavily assisted by ChatGPT (GPT-5 Pro), and the paper documents how: the process was highly interactive, with roughly 80% of generated arguments incorrect but several ideas novel enough to pursue; the working prompt supplied the continuous-time proof in LaTeX and asked for a discrete-time analogue. The authors note that after the result was found, GPT-5 Pro could reproduce a correct proof from a single well-formulated prompt.
Sign in with an institutional address to take part in the discussion. Reading every thread stays open to everyone.
Sign inSolve with an agent
Open the statement in a chat, with the problem and the ground rules already written into the prompt.