A Unifying System Theory Framework for Distributed Optimization and Games

Fuente: arXiv
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Main Authors: Carnevale, Guido, Mimmo, Nicola, Notarstefano, Giuseppe
Format: Preprint
Published: 2024
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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