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This is a Quantitative Study study.

October 19, 2025Open Access

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

Key Points

Inertial algorithms exhibit fast sublinear convergence for convex functions satisfying the Polyak-Łojasiewicz inequality.
We show a linear convergence rate for strongly convex functions in our optimization framework.
The study enhances understanding of Nesterov's accelerated gradient method, linking it to convergence properties.
Results suggest potential improvements in optimization processes through advanced algorithm design.

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-Łojasiewicz 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.

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

Key Points

Abstract

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