Primal-Dual Subgradient Algorithm for Distributed Constraint Optimization Over Unbalanced Digraphs

This paper investigates the distributed convex optimization problem with coupled inequality constraints over unbalanced digraphs depicted as row-stochastic matrices, where each agent in the network only has access to its local information, while the local constraint functions of all the agents are coupled in inequality constraints. To solve this kind of problems, a novel distributed iterative algorithm is proposed via consensus scheme and the projected primal-dual subgradient method. Different from the previous related results, our algorithm can not only deal with coupling inequality constraints but also conquer the unbalanced topology caused by directed graphs. Moreover, it is proved that under certain assumptions, the optimal solution of the problem can be asymptotically obtained by performing the designed algorithm. Finally, the numerical examples are presented to further illustrate the efficacy of the proposed approach.