Distributed Convex Optimization With Coupling Constraints Over Time-Varying Directed Graphs

Abstract

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