{"ID":2847692,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.27645","arxiv_id":"2510.27645","title":"Convergence Analysis of Distributed Optimization: A Dissipativity Framework","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.","short_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 yi...","url_abs":"https://arxiv.org/abs/2510.27645","url_pdf":"https://arxiv.org/pdf/2510.27645v2","authors":"[\"Aron Karakai\",\"Jaap Eising\",\"Andrea Martinelli\",\"Florian Dörfler\"]","published":"2025-10-31T17:19:17Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}