Distributed projection-free algorithm for constrained aggregative optimization

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.