  In this paper, we investigate a distributed aggregative optimization problem
in a network, where each agent has its own local cost function which depends
not only on the local state variable but also on an aggregated function of
state variables from all agents. To accelerate the optimization process, we
combine heavy ball and Nesterov's accelerated methods with distributed
aggregative gradient tracking, and propose two novel algorithms named DAGT-HB
and DAGT-NES for solving the distributed aggregative optimization problem. We
analyse that the DAGT-HB and DAGT-NES algorithms can converge to an optimal
solution at a global $\mathbf{R}-$linear convergence rate when the objective
function is smooth and strongly convex, and when the parameters (e.g., step
size and momentum coefficients) are selected within certain ranges. A numerical
experiment on the optimal placement problem is given to verify the
effectiveness and superiority of our proposed algorithms.
