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<p>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 (<i>e.g.</i>, 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.</p>

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Near-optimal Closed-loop Method via Lyapunov Damping

  • 期刊论文

  • 发表日期：

    2026年2月11日

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  • Severin Maier,
  • Camille Castera,
  • Peter Ochs

摘要

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.