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First order optimization methods based on Hessian-driven Nesterov accelerated gradient flow

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arxiv 1912.09276 v2 pith:7UDO6MSB submitted 2019-12-19 math.OC

classification math.OC
keywords acceleratedflownesterovoptimizationconvexexplicitgradienth-nag
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A novel dynamical inertial Newton system, which is called Hessian-driven Nesterov accelerated gradient (H-NAG) flow is proposed. Convergence of the continuous trajectory are established via tailored Lyapunov function, and new first-order accelerated optimization methods are proposed from ODE solvers. It is shown that (semi-)implicit schemes can always achieve linear rate and explicit schemes have the optimal(accelerated) rates for convex and strongly convex objectives. In particular, Nesterov's optimal method is recovered from an explicit scheme for our H-NAG flow. Furthermore, accelerated splitting algorithms for composite optimization problems are also developed.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. HNAG$^{++}$: An Accelerated Gradient Method with a Refined Asymptotic Rate for Strongly Convex Optimization

    math.OC 2025-10 conditional novelty 7.0 of 10

    A Lyapunov/ODE-based analysis yields HNAG+ (rate 1-2/√κ) and HNAG++ (asymptotic rate 1-2√(2/κ) under Hölder Hessians).

  2. Continuous and discrete-time accelerated methods for an inequality constrained convex optimization problem

    math.OC 2024-11 conditional novelty 5.0 of 10

    A Bregman Lagrangian with a logarithmic barrier leads to a continuous-time dynamical system and discrete accelerated methods that converge to the solution of convex inequality-constrained problems.

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