{"ID":2853042,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.16680","arxiv_id":"2510.16680","title":"HNAG$^{++}$: An Accelerated Gradient Method with a Refined Asymptotic Rate for Strongly Convex Optimization","abstract":"Two accelerated first-order methods, HNAG$^+$ and HNAG$^{++}$, are presented for smooth strongly convex optimization. By optimizing the coercivity constant of the HNAG flow and using a refined Lyapunov analysis, it is shown that HNAG$^+$ achieves the optimal global rate $1-2/\\sqrtκ$, matching the information-theoretic lower bound for strongly convex optimization. For functions with Local Asymptotic Symmetry at the minimizer, HNAG$^{++}$ is shown to achieve the asymptotic rate $1-2\\sqrt{2/κ}$, matching the best known asymptotic rate under $\\mathcal C^2$ regularity, while applying to a broader local function class. Numerical experiments on linear and nonlinear examples show that the proposed methods are competitive with existing accelerated schemes.","short_abstract":"Two accelerated first-order methods, HNAG$^+$ and HNAG$^{++}$, are presented for smooth strongly convex optimization. By optimizing the coercivity constant of the HNAG flow and using a refined Lyapunov analysis, it is shown that HNAG$^+$ achieves the optimal global rate $1-2/\\sqrtκ$, matching the information-theoretic...","url_abs":"https://arxiv.org/abs/2510.16680","url_pdf":"https://arxiv.org/pdf/2510.16680v2","authors":"[\"Long Chen\",\"Zeyi Xu\"]","published":"2025-10-19T01:21:01Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}