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.

翻译：本文研究网络中一类分布式聚合优化问题，其中每个智能体具有依赖于自身局部状态变量及所有智能体状态变量聚合函数的局部代价函数。为加速优化过程，我们将重球法和涅斯捷罗夫加速方法与分布式聚合梯度追踪相结合，提出两种新型算法——DAGT-HB和DAGT-NES，用于求解分布式聚合优化问题。我们分析表明，当目标函数光滑且强凸，且参数（如步长和动量系数）选取在特定范围内时，DAGT-HB和DAGT-NES算法能以全局$\mathbf{R}-$线性收敛速率收敛至最优解。通过最优布局问题的数值实验验证了所提算法的有效性和优越性。