Distributed continuous-time proximal algorithm for nonsmooth resource allocation problem with coupled constraints

This paper studies the distributed resource allocation problem with nonsmooth local cost functions subject to the coupled equality and inequality constraints. In particular, each local cost function is expressed as the sum of a differentiable function and two nonsmooth functions. By using the operator splitting and primal–dual method, a continuous-time distributed proximal algorithm is developed, which can be applied to more general local cost functions that are convex but not necessarily smooth. In addition, the proposed algorithm is fully distributed in the sense that the gain parameter can be determined locally and does not require any global information of the network. By applying Lyapunov stability analysis and convex optimization theory, it is shown that the decision variables of all the agents converge to an optimal solution. Finally, a simulation example is carried out to demonstrate the effectiveness of the proposed algorithm.