Accelerated Distributed Aggregative Optimization
Jiaxu Liu, Song Chen, Shengze Cai, Chao Xu, Jian Chu · IEEE Transactions on Automatic Control · 2025
This article delves into the investigation of a distributed aggregative optimization problem within a network. In this scenario, each agent possesses its own local cost function, which relies not only on the local state variable but also on an aggregated function of state variables from all agents. To expedite the optimization process, we amalgamate the heavy ball and Nesterov's accelerated method with distributed aggregative gradient tracking, resulting in the proposal of two innovative algorithms, aimed at resolving the distributed aggregative optimization problem. Our analysis demonstrates that the proposed algorithms can converge to an optimal solution at a global linear convergence rate when the objective function is strongly convex with the Lipschitz-continuous gradient, and when the parameters (e.g., step size and momentum coefficients) are chosen within specific ranges. In addition, we present several numerical experiments to verify the effectiveness, robustness, and superiority of our proposed algorithms.