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arXiv · 2510.27645

Convergence Analysis of Distributed Optimization: A Dissipativity Framework

Aron Karakai·Jaap Eising·Andrea Martinelli·Florian Dörfler
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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.

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Aron Karakai, Jaap Eising, Andrea Martinelli, Florian Dörfler. 2025-10-31. Convergence Analysis of Distributed Optimization: A Dissipativity Framework. https://arxiv.org/abs/2510.27645

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