Decentralized Schemes with Overlap for Solving Graph-Structured Optimization Problems

TL;DR

This paper introduces a decentralized optimization algorithm for graph-structured problems that uses overlapping subdomains to enhance convergence speed, bridging decentralized and centralized methods with practical advantages.

Contribution

It proposes a novel overlapping subdomain approach that accelerates convergence and supports flexible, asynchronous, and privacy-preserving implementations in decentralized network systems.

Findings

Convergence improves exponentially with overlap size.

The method outperforms ADMM in large power network estimation.

Supports asynchronous execution and constraint handling.

Abstract

We present a new algorithmic paradigm for the decentralized solution of graph-structured optimization problems that arise in the estimation and control of network systems. A key and novel design concept of the proposed approach is that it uses overlapping subdomains to promote and accelerate convergence. We show that the algorithm converges if the size of the overlap is sufficiently large and that the convergence rate improves exponentially with the size of the overlap. The proposed approach provides a bridge between fully decentralized and centralized architectures and is flexible in that it enables the implementation of asynchronous schemes, handling of constraints, and balancing of computing, communication, and data privacy needs. The proposed scheme is tested in an estimation problem for a 9241-node power network and we show that it outperforms the alternating direction method of multipliers.