Accelerated distributed online aggregative optimization over unbalanced digraphs

This paper investigates online distributed aggregative optimization of multi-agent systems over directed graphs characterized by row-stochastic mixing matrices, where each agent possesses a time-varying cost function determined by its individual decision variable and a global aggregative variable. To address this problem, we first propose a novel accelerated distributed algorithm incorporating gradient tracking and dynamic consensus mechanisms. Then, the designed algorithm integrates heavy-ball momentum to enhance convergence speed, and the linear convergence rate is rigorously analyzed as well. Finally, the theoretical results are validated in the multi-robot target tracking scenarios to show the effectiveness of the algorithm.