A Unifying System Theory Framework for Distributed Optimization and Games
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915299062710272 |
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| author | Carnevale, Guido Mimmo, Nicola Notarstefano, Giuseppe |
| author_facet | Carnevale, Guido Mimmo, Nicola Notarstefano, Giuseppe |
| contents | This paper introduces a systematic methodological framework to design and analyze distributed algorithms for optimization and games over networks. Starting from a centralized method, we identify an aggregation function involving all the decision variables (e.g., a global cost gradient or constraint) and introduce a distributed consensus-oriented scheme to asymptotically approximate the unavailable information at each agent. Then, we delineate the proper methodology for intertwining the identified building blocks, i.e., the optimization-oriented method and the consensus-oriented one. The key intuition is to interpret the obtained interconnection as a singularly perturbed system. We rely on this interpretation to provide sufficient conditions for the building blocks to be successfully connected into a distributed scheme exhibiting the convergence guarantees of the centralized algorithm. Finally, we show the potential of our approach by developing a new distributed scheme for constraint-coupled problems with a linear convergence rate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12623 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Unifying System Theory Framework for Distributed Optimization and Games Carnevale, Guido Mimmo, Nicola Notarstefano, Giuseppe Optimization and Control This paper introduces a systematic methodological framework to design and analyze distributed algorithms for optimization and games over networks. Starting from a centralized method, we identify an aggregation function involving all the decision variables (e.g., a global cost gradient or constraint) and introduce a distributed consensus-oriented scheme to asymptotically approximate the unavailable information at each agent. Then, we delineate the proper methodology for intertwining the identified building blocks, i.e., the optimization-oriented method and the consensus-oriented one. The key intuition is to interpret the obtained interconnection as a singularly perturbed system. We rely on this interpretation to provide sufficient conditions for the building blocks to be successfully connected into a distributed scheme exhibiting the convergence guarantees of the centralized algorithm. Finally, we show the potential of our approach by developing a new distributed scheme for constraint-coupled problems with a linear convergence rate. |
| title | A Unifying System Theory Framework for Distributed Optimization and Games |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2401.12623 |