Differentially Private Distributed Optimization with Coupled Inequality Constraints

This article explores differential privacy in distributed optimization problems(DOPs) involving coupled equality and inequality constraints, where multiple agents cooperates to minimize a global objective function. By adding DP-noise into the exchanged iteration variables of a primal-dual algorithm, we develop a differentially-private distributed algorithm ensuring both accurate convergence and rigorous ϵ-differential privacy(ϵ-DP) over infinite iterations. The developed algorithm does not require the objective functions to be strong convex, or impose assumptions on the boundedness regarding the gradient of cost functions. Furthermore, we establish provable results on the convergence and privacy guarantees under both diminishing and constant step-sizes, and provide theoretical analyses of the trade-off between the accuracy of convergence and the strength of privacy protection. Finally, numerical simulations are carried out to assess the validity of the developed algorithm.