Near-optimal Closed-loop Method via Lyapunov Damping for Convex Optimization

Severin Maier; Camille Castera; Peter Ochs

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arXiv · 2311.10053

Near-optimal Closed-loop Method via Lyapunov Damping for Convex Optimization

Severin Maier·Camille Castera·Peter Ochs

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Abstract

We introduce an autonomous system with closed-loop damping for first-order convex optimization. While, to this day, optimal rates of convergence are almost exclusively achieved by non-autonomous methods via open-loop damping (e.g., Nesterov's algorithm), we show that our system, featuring a closed-loop damping, exhibits a rate arbitrarily close to the optimal one. We do so by coupling the damping and the speed of convergence of the system via a well-chosen Lyapunov function. By discretizing our system we then derive an algorithm and present numerical experiments supporting our theoretical findings.

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BibTeX RIS

Severin Maier, Camille Castera, Peter Ochs. 2023-11-16. Near-optimal Closed-loop Method via Lyapunov Damping for Convex Optimization. https://arxiv.org/abs/2311.10053

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