Continuous-time algorithm for distributed resource allocation over a weight-unbalanced digraph

This paper studies a resource allocation problem subject to the coupling resource constraint over a strongly connected and weight-unbalanced digraph, where the global cost function is composed of a sum of the agents’s local cost functions. To solve the problem in a distributed way, we design a continuous-time algorithm by injecting a graph balancing technique into a primal-dual gradient flow algorithm. We show that the optimal variable generated by the proposed algorithm asymptotically converges to the optimal solution when the local cost functions are strongly convex and and their gradients satisfy Lipschitz conditions. A numerical simulation verifies the theoretical result.