Distributed Constrained Optimization over Networked Systems via A Singular Perturbation Method

TL;DR

This paper introduces a fully distributed algorithm for constrained optimization in networked systems, combining singular perturbation, consensus, and saddle point methods, with proven optimality and privacy guarantees, demonstrated through energy network simulations.

Contribution

It presents a novel distributed optimization algorithm using singular perturbation and saddle point dynamics for general objectives and constraints, ensuring privacy and optimality.

Findings

Guarantees privacy of agents' information.

Proves convergence to optimal solutions.

Validated through energy network simulations.

Abstract

This paper studies a constrained optimization problem over networked systems with an undirected and connected communication topology. The algorithm proposed in this work utilizes singular perturbation, dynamic average consensus, and saddle point dynamics methods to tackle the problem for a general class of objective function and affine constraints in a fully distributed manner. It is shown that the private information of agents in the interconnected network is guaranteed in our proposed strategy. The theoretical guarantees on the optimality of the solution are provided by rigorous analyses. We apply the new proposed solution into energy networks by a demonstration of two simulations.