{"ID":2825891,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.20478","arxiv_id":"2512.20478","title":"Adaptive Accelerated Gradient Method for Smooth Convex Optimization","abstract":"We propose an adaptive accelerated gradient method for solving smooth convex optimization problems. The method incorporates a scheme to determine the step size adaptively, by means of a local estimation of the smoothness constant, which is assumed unknown, without resorting to line search procedures. The sequence generated by this method converges weakly to a minimizer of the objective function, and the function values converge at a fast rate of $\\mathcal{O}\\left( \\frac{1}{k^2} \\right)$. Moreover, if the objective function is strongly convex, the function values converge at a linear rate.","short_abstract":"We propose an adaptive accelerated gradient method for solving smooth convex optimization problems. The method incorporates a scheme to determine the step size adaptively, by means of a local estimation of the smoothness constant, which is assumed unknown, without resorting to line search procedures. The sequence gener...","url_abs":"https://arxiv.org/abs/2512.20478","url_pdf":"https://arxiv.org/pdf/2512.20478v1","authors":"[\"Zepeng Wang\",\"Juan Peypouquet\"]","published":"2025-12-23T16:13:27Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}