Privacy Preserving Distributed Algorithm for Constrained Resource Allocation Problems with Communication Delays

This article investigates a constraint-coupled resource allocation problem, where each node has its own cost function and communicates with its neighbors to tackle the optimization problem cooperatively. However, the communication environment is non-ideal, so the nodes will suffer from communication delay and potential information leakage. Therefore, a privacy-preserving mismatch-tracking algorithm with communication delay is proposed. To address communication delays, virtual nodes are introduced to transform the original delayed algorithm into a delay-free augmented system. It is then proved that the algorithm can achieve a linear convergence rate with proper constant step size for strongly convex and smooth cost functions. Furthermore, the convergence accuracy and privacy level of the algorithm are characterized. Finally, a simulation example is provided to validate the theoretical results and demonstrate the effectiveness of the algorithm.