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 $1-2/\sqrt{\kappa}$, 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 $1-2\sqrt{2/\kappa}$, 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.
From: Zeyi Xu [view email]
[v1]
Sun, 19 Oct 2025 01:21:01 UTC (1,367 KB)
[v2]
Thu, 28 May 2026 17:12:44 UTC (794 KB)
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