  In this paper, we focus on solving a distributed convex aggregative
optimization problem in a network, where each agent has its own cost function
which depends not only on its own decision variables but also on the aggregated
function of all agents' decision variables. The decision variable is
constrained within a feasible set. In order to minimize the sum of the cost
functions when each agent only knows its local cost function, we propose a
distributed Frank-Wolfe algorithm based on gradient tracking for the
aggregative optimization problem where each node maintains two estimates,
namely an estimate of the sum of agents' decision variable and an estimate of
the gradient of global function. The algorithm is projection-free, but only
involves solving a linear optimization to get a search direction at each step.
We show the convergence of the proposed algorithm for convex and smooth
objective functions over a time-varying network. Finally, we demonstrate the
convergence and computational efficiency of the proposed algorithm via
numerical simulations.
