تقرير
Near-optimal Closed-loop Method via Lyapunov Damping for Convex Optimization
| العنوان: | Near-optimal Closed-loop Method via Lyapunov Damping for Convex Optimization |
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| المؤلفون: | Maier, Severin, Castera, Camille, Ochs, Peter |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Optimization and Control, Computer Science - Machine Learning, Mathematics - Dynamical Systems |
| الوصف: | 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. |
| نوع الوثيقة: | Working Paper |
| الوصول الحر: | http://arxiv.org/abs/2311.10053Test |
| رقم الانضمام: | edsarx.2311.10053 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |