An Asynchronous Gradient Descent Based Method for Distributed Resource Allocation With Bounded Variables

This article considers the distributed resource allocation problem over a network of n agents with individual optimization functions and coupled resource constraints. The optimization variables are bounded for each agent. We propose an asynchronous distributed gradient descent based method, which is able to tackle time-varying communication networks and communication problems. The main ideas are twofold. First, the degree of freedom of the network is reduced to deal with the global constraint. Second, we utilize delay compensation to counteract the delay of asynchronous communication. We prove that the convergence rate is $O(\frac{1}{k})$ and analyze both the communication complexity and the time complexity. This method is applied into the parallel pump control problem in HVAC system and shows good numerical results.