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

arXiv:2311.10053v2 Announce Type: replace-cross
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 …

abstract algorithm arxiv autonomous convergence cs.lg loop math.ds math.oc near optimization rate show type via