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arXiv · 2506.21730

Fast convex optimization via inertial systems with asymptotically vanishing viscosity and Hessian-driven damping

Zepeng Wang·Juan Peypouquet
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Abstract

We study the convergence rate of a family of inertial algorithms, which can be obtained by discretization of an inertial system combining asymptotic vanishing viscous and Hessian-driven damping. We establish a fast sublinear convergence rate in case the objective function is convex and satisfies Polyak-\L ojasiewicz inequality. We also establish a linear convergence rate for strongly convex functions. The results can provide more insights into the convergence property of Nesterov's accelerated gradient method.

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Zepeng Wang, Juan Peypouquet. 2025-06-26. Fast convex optimization via inertial systems with asymptotically vanishing viscosity and Hessian-driven damping. https://arxiv.org/abs/2506.21730

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