EUROPT 2025
Abstract Submission

180. A Speed Restart Scheme for an Inertial System with Hessian-Driven Damping and Three Constant Coefficients

Invited abstract in session TB-9: Variational Analysis I, stream Variational analysis: theory and algorithms.

Tuesday, 10:30-12:30
Room: B100/8013

Authors (first author is the speaker)

1. Huiyuan Guo
2. Juan Jose Maulen
Center for Mathematical Modeling, University of Chile
3. Juan Peypouquet
Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen

Abstract

The use of inertial methods is a popular first-order approach to smooth convex optimization problems. Numerous algorithms and methods have been proposed, gradient method, heavy ball with friction, Newton's method and so on. In recent years, researchers start to analyze the related differential equations or inclusions for investigating the dynamic behavior of these iterative algorithms. Despite the fast convergence rate guarantee, the trajectories as well as the sequences generated by inertial first-order methods exhibit chaotic behavior. Restart techniques represent an alternative way to accelerate gradient methods by reducing the oscillations. We analyze a speed restart scheme for an inertial system with Hessian-driven damping and three constant coefficients. We establish a linear convergence rate for the function values along the restarted trajectories without assuming the strong convexity of the objective function. We also report numerical experiments which show that dynamical system with speed restarting scheme together improve the performance of both continuous dynamics and inertial algorithms as a heuristic.

Keywords

Status: accepted


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