Discoveries / algorithms-optimization

Point Convergence of Nesterov's Accelerated Gradient Method

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.