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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.27645 |
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| _version_ | 1866915930760544256 |
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| author | Karakai, Aron Eising, Jaap Martinelli, Andrea Dörfler, Florian |
| author_facet | Karakai, Aron Eising, Jaap Martinelli, Andrea Dörfler, Florian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_27645 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence Analysis of Distributed Optimization: A Dissipativity Framework Karakai, Aron Eising, Jaap Martinelli, Andrea Dörfler, Florian Optimization and Control 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. |
| title | Convergence Analysis of Distributed Optimization: A Dissipativity Framework |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2510.27645 |