In this paper, we investigate a distributed aggregative optimization problem in a network, where each agent has its own local cost function which depends not only on the local state variable but also on an aggregated function of state variables from all agents. To accelerate the optimization process, we combine heavy ball and Nesterov's accelerated methods with distributed aggregative gradient tracking, and propose two novel algorithms named DAGT-HB and DAGT-NES for solving the distributed aggregative optimization problem. We analyse that the DAGT-HB and DAGT-NES algorithms can converge to an optimal solution at a global $\mathbf{R}-$linear convergence rate when the objective function is smooth and strongly convex, and when the parameters (e.g., step size and momentum coefficients) are selected within certain ranges. A numerical experiment on the optimal placement problem is given to verify the effectiveness and superiority of our proposed algorithms.

本文研究了在网络中分布式汇聚优化问题，提出了结合重球和Nesterov加速方法的分布式汇聚梯度跟踪的两个新算法DAGT-HB和DAGT-NES，分析这两个算法在目标函数光滑，强凸且参数选择在一定范围内时，能以全局R线性收敛速度收敛到最优解，通过最优放置问题的数值实验验证了算法的有效性和优越性。

加速分布式聚合优化