Distributed Aggregative Optimization via Finite-Time Dynamic Average Consensus

This paper studies the distributed aggregative optimization problem with local constraint sets over an undirected graph. The local objective function of each agent depends on its own decision variables and an aggregation function composed of all agents' decision variables. Taking advantage of the dynamic average consensus method and the projection operator, a continuous-time algorithm with nonuniform gradient gains is proposed to seek the optimal decision variable, which only requires the sign of relative state information between agents' neighbours and has an advantage in reducing communication cost. It is proved that auxiliary variables for estimating the aggregation function achieve consensus in finite time and the proposed algorithm converges asymptotically to the optimal decision variable based on the Lyapunov stability theory. Finally, numerical examples are provided to show the effectiveness of theoretical results.