  This paper 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 average
of summable functions of decision variables of all other agents. To handle this
problem, a distributed algorithm, called distributed gradient tracking (DGT),
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.
