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A Unifying System Theory Framework for Distributed Optimization and Games
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AI
DOI：10.1109/TAC.2025.3573800.png)
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Abstract
En 中文
This article 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.
Keywords:
Distributed optimization
game theory
network analysis and control
optimization algorithms
Journal
IF:
7
Papers:
1.3W
Citations:
6.7W