Mathematical Optimization for Data Science Group, Saarland University

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Department of Mathematics and Computer Science, Saarland University, Germany

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

S. Maier, C. Castera and P. 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 only achieved by non-autonomous methods via open-loop damping (e.g., Nesterov's algorithm), we show that our system is the first one featuring a closed-loop damping while exhibiting 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. We then derive a practical first-order algorithm called LYDIA by discretizing our system, and present numerical experiments supporting our theoretical findings.



pdf	Bibtex	arXiv

Latest update: 21.11.2023

Citation:
S. Maier, C. Castera, P. Ochs:
Near-optimal Closed-loop Method via Lyapunov Damping for Convex Optimization.

Technical Report, ArXiv e-prints, arXiv:2311.10053, 2023.

Bibtex:
@techreport{MCO23, title = {Near-optimal Closed-loop Method via Lyapunov Damping for Convex Optimization}, author = {S. Maier and C. Castera and P. Ochs}, year = {2023}, journal = {ArXiv e-prints, arXiv:2311.10053}, }

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