{"ID":2850069,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.22715","arxiv_id":"2510.22715","title":"The Iterates of Nesterov's Accelerated Algorithm Converge in The Critical Regimes","abstract":"In this paper, we prove that the iterates of the accelerated Nesterov's algorithm in the critical regime do converge in the weak topology to a global minimizer of an $L$-smooth function in a real Hilbert space, hence answering positively a conjecture posed by H. Attouch and co-authors a decade ago. This result is the algorithmic case of a very recent result on the continuous-time system posted by E. Ryu on X, with assistance from ChatGPT.","short_abstract":"In this paper, we prove that the iterates of the accelerated Nesterov's algorithm in the critical regime do converge in the weak topology to a global minimizer of an $L$-smooth function in a real Hilbert space, hence answering positively a conjecture posed by H. Attouch and co-authors a decade ago. This result is the a...","url_abs":"https://arxiv.org/abs/2510.22715","url_pdf":"https://arxiv.org/pdf/2510.22715v2","authors":"[\"Radu Ioan Bot\",\"Jalal Fadili\",\"Dang-Khoa Nguyen\"]","published":"2025-10-26T15:19:19Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}