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 ob jective sub ject to local constraints and global coupling constraints. Over directed graphs, we propose a distributed algorithm that incorporates the push-sum protocol into dual sub-gradient methods. Under the convexity assumption, the optimality of primal and dual variables, and the constraint violation are first established. Then the explicit convergence rates of the proposed algorithm are obtained. Finally, numerical experiments on the economic dispatch problem are provided to demonstrate the efficacy of the proposed algorithm.