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arXiv · 2506.11267

Towards faster first order methods: A continuous-time model to interpolate between speed and function value restart

Juan José Maulén·Huiyuan Guo·Juan Peypouquet
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Abstract

We introduce a new restarting scheme for a continuous inertial dynamics with Hessian driven-damping, and establish a linear convergence rate for the function values along the restarted trajectories. The proposed routine is implemented without knowing the strong convexity parameter, and is a generalization of existing speed restart schemes. It interpolates between speed and function value restarts, considerably delaying the restarting time, while preserving convergence and function value decrease. Numerical experiments show an improvement in the convergence rates for both continuous-time dynamical systems, and the associated accelerated first-order algorithms derived via time discretization.

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Juan José Maulén, Huiyuan Guo, Juan Peypouquet. 2025-06-12. Towards faster first order methods: A continuous-time model to interpolate between speed and function value restart. https://arxiv.org/abs/2506.11267

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