# A Unifying System Theory Framework for Distributed Optimization and Games

arXiv: https://arxiv.org/abs/2401.12623 · HTML: https://mlsanity.com/paper/2401.12623/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2024.

## Built on by (most cited first, 1 of 1)

- [Towards a Systems Theory of Algorithms](https://mlsanity.com/paper/2401.14029/) (2024)

## Abstract (arXiv)

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.