Distributed convex optimization with coupling constraints over time-varying directed graphs^†

This paper considers a distributed convex optimization problem over time-varying multi-agent network, where each agent has its own decision variables that should be set so as to minimize individual objective subject local constraints and global coupling constraints. Over directed graphs, we propose algorithm incorporates the push-sum protocol into dual sub-gradient methods. Under convexity assumption, optimality of primal variables, constraint violation are first established. Then explicit convergence rates proposed obtained. Finally, numerical experiments on economic dispatch provided demonstrate efficacy algorithm.