Privacy-Preserving Dual Stochastic Push-Sum Algorithm for Distributed Constrained Optimization

This paper investigates a private distributed optimization problem over a multi-agent network, where the goal is to cooperatively minimize the sum of all locally convex cost functions subject to coupled equality constraints over time-varying unbalanced directed networks while considering privacy concerns. To solve this problem, we integrate push-sum protocols with dual subgradient methods to design a private distributed dual stochastic push-sum algorithm. Under the assumption of convexity, we first establish the convergence of the algorithm in terms of dual variables, primal variables and constraint violations. Then we show that the algorithm has a sub-linear growth with order of $$O(\ln t/\sqrt{t})$$ O ( ln t / t ) . The result reveals that there is a tradeoff between the privacy level and the accuracy of the algorithm. Finally, the efficiency of the algorithm is verified numerically over two applications to the economic dispatch problems and electric vehicles charging control problems.