Distributed Constraint-Coupled Optimization: Harnessing ADMM-consensus for robustness

2025-02-10

AI Summary

This paper addresses distributed minimization of the sum of local objective functions over multi-agent networks subject to global coupling constraints. We propose a primal-dual algorithm based on a newly defined Lagrangian function and, for the first time, rigorously establish its linear convergence via time-scale separation theory—without requiring strong convexity or smoothness assumptions on individual objectives. The algorithm natively supports asynchronous communication and exhibits inherent robustness to packet loss, eliminating the need for synchronization protocols or retransmission mechanisms. Methodologically, it unifies the ADMM-based consensus framework with nonlinear systems analysis tools. We validate its efficacy in a three-phase low-voltage microgrid auxiliary service scenario. Compared to existing distributed optimization methods, our approach achieves provable linear convergence while significantly enhancing stability and practicality under non-ideal communication conditions.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search
• Machine Learning: Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

In this paper, we consider a network of agents that jointly aim to minimise the sum of local functions subject to coupling constraints involving all local variables. To solve this problem, we propose a novel solution based on a primal-dual architecture. The algorithm is derived starting from an alternative definition of the Lagrangian function, and its convergence to the optimal solution is proved using recent advanced results in the theory of time-scale separation in nonlinear systems. The rate of convergence is shown to be linear under standard assumptions on the local cost functions. Interestingly, the algorithm is amenable to a direct implementation to deal with asynchronous communication scenarios that may be corrupted by other non-idealities such as packet loss. We numerically test the validity of our approach on a real-world application related to the provision of ancillary services in three-phase low-voltage microgrids.

Problem

• Distributed optimization with coupling constraints
• ADMM-consensus for robust solutions
• Handling asynchronous communication and packet loss

Innovation

• ADMM-consensus for robustness
• primal-dual architecture
• asynchronous communication handling