In this study, we introduce a distributed algorithm that is specifically designed to address optimization problems featuring a decomposable objective function and equality constraints. To minimize the amount of communication required, we incorporate an event-triggered mechanism that enables information exchange only when variable values exceed predefined thresholds. Importantly, our proposed algorithm possesses a distinctive characteristic where the determination of step size is solely based on the properties of the objective function, regardless of the structure of the communication network. Even in situations where changes occur in the network structure, our algorithm remains valid without necessitating any updates to its step size. Assuming strong convexity and smoothness in local objective functions, along with appropriate event-triggered thresholds, our algorithm achieves a convergence rate that is linear. Several numerical experiments provide evidence supporting the effectiveness and superiority of our proposed approach.

在本研究中，我们引入了一种分布式算法，该算法专门用于解决具有可分解目标函数和等式约束的优化问题。为了最大限度地减少所需的通信量，我们采用了事件触发机制，仅当变量值超过预定义阈值时才启用信息交换。重要的是，我们提出的算法具有一个独特的特征，即步长的确定仅基于目标函数的属性，而与通信网络的结构无关。即使在网络结构发生变化的情况下，我们的算法仍然有效，无需对其步长进行任何更新。假设局部目标函数具有很强的凸性和平滑性，以及适当的事件触发阈值，我们的算法实现了线性收敛率。几个数值实验提供了支持我们提出的方法的有效性和优越性的证据。