Distributed Aggregative Optimization Over Multi-Agent Networks

This article proposes a new framework for distributed optimization, called distributed aggregative optimization, which allows local objective functions to be dependent not only on their own decision variables, but also on the sum of functions of decision variables of all the agents. To handle this problem, a distributed algorithm, called distributed aggregative gradient tracking, is proposed and analyzed, where the global objective function is strongly convex, and the communication graph is balanced and strongly connected. It is shown that the algorithm can converge to the optimal variable at a linear rate. A numerical example is provided to corroborate the theoretical result.