{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/near-optimal-closed-loop-method-via-lyapunov","title":"Near-optimal Closed-loop Method via Lyapunov Damping for Convex Optimization","arxiv_id":"2311.10053","date":"2023-11-16","proceeding":null,"authors":["Severin Maier","Camille Castera","Peter Ochs"],"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.","url_abs":"https://arxiv.org/abs/2311.10053v2","url_pdf":"https://arxiv.org/pdf/2311.10053v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"near-optimal-closed-loop-method-via-lyapunov","repo_url":"https://github.com/camcastera/lydia","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[{"method_slug":"speed","method_name":"SPEED"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}