This article considers a problem of solving the optimal solution of the sum of locally convex cost functions over an undirected network. Each local convex cost function in the network is accessed only by each unit. To be able to reduce the amount of computation and get the desired result in an accelerated way, we put forward a fresh accelerated decentralized event-triggered algorithm, named as A-DETA, for the optimization problem. A-DETA combines gradient tracking and two momentum accelerated terms, adopts nonuniform step-sizes and emphasizes that each unit interacts with neighboring units independently only at the sampling time triggered by the event. On the premise of assuming the smoothness and strong convexity of the cost function, it is proved that A-DETA can obtain the exact optimal solution linearly in the event of sufficiently small positive step-size and momentum coefficient. Moreover, an explicit linear convergence speed is definitely shown. Finally, extensive simulation example validates the usability of A-DETA.

中文翻译：

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去中心化事件触发凸优化算法的加速收敛

本文考虑在无向网络上求解局部凸成本函数之和的最优解的问题。网络中的每个局部凸成本函数只能由每个单元访问。为了能够减少计算量并以加速的方式获得期望的结果，我们针对优化问题提出了一种全新的加速分散事件触发算法，称为A-DETA。A-DETA 结合了梯度跟踪和两个动量加速项，采用非均匀步长，强调每个单元仅在事件触发的采样时间与相邻单元独立交互。在假设代价函数的平滑性和强凸性的前提下，证明了在正步长和动量系数足够小的情况下，A-DETA 可以线性地得到精确的最优解。此外，明确显示了明确的线性收敛速度。最后，广泛的仿真示例验证了 A-DETA 的可用性。