Convergence Analysis of Distributed Optimization: A Dissipativity Framework
Optimization and Control
2026-04-14 v2
Abstract
We develop a system-theoretic framework for the structured analysis of distributed optimization algorithms with decomposable cost functions. We model such algorithms as a network of interacting dynamical systems and derive tests for convergence based on incremental dissipativity and contraction theory. This approach yields a step-by-step analysis pipeline suitable for any network structure, with conditions expressed as linear matrix inequalities. In addition, a numerical comparison with traditional analysis methods is presented, in the context of distributed gradient descent.
Cite
@article{arxiv.2510.27645,
title = {Convergence Analysis of Distributed Optimization: A Dissipativity Framework},
author = {Aron Karakai and Jaap Eising and Andrea Martinelli and Florian Dörfler},
journal= {arXiv preprint arXiv:2510.27645},
year = {2026}
}
Comments
Note: This paper has been accepted for presentation at the 2026 European Control Conference (ECC)