  In this work, we consider solving a distributed optimization problem in a
multi-agent network with multiple clusters. In each cluster, the involved
agents cooperatively optimize a separable composite function with a common
decision variable. Meanwhile, a global cost function of the whole network is
considered associated with an affine coupling constraint across the clusters.
To solve this problem, we propose a cluster-based dual proximal gradient
algorithm by resorting to the dual problem, where the global cost function is
optimized when the agents in each cluster achieve an agreement on the optimal
strategy and the global coupling constraint is satisfied. In addition, the
proposed algorithm allows the agents to only communicate with their immediate
neighbors. The computational complexity of the proposed algorithm with
simple-structured cost functions is discussed and an ergodic convergence with
rate O(1/T) is guaranteed (T is the index of iterations).
