Distributed Event-Triggered Algorithm Designs for Resource Allocation Problems via a Universal Scalar Function-Based Analysis

In this article, we are concerned with distributed algorithm designs for resource allocation problems via event-triggered communication. The target is to search an optimal resource allocation scheme such that the summation of $n(>1)$ objective functions is minimized. Due to communication efficiency and privacy concerns, distributed algorithms with event-triggered communications are proposed in this article. The communication is only permitted or triggered if variation of gradient of the local objective function exceeds a threshold. By constructing a novel technical lemma and a universal scalar function, the convergence and linear convergence rates are established under some mild assumptions. Extensive numerical experiments on the IEEE 118-bus power system demonstrate that: Compared to the periodic algorithms, such as ADMM and Mirror-P-EXTRA, the proposed algorithms not only remarkably reduce the communication times but also have competitive convergence speed. The latter is striking that it implies there exist useless communications in the periodic algorithms that are censored by the proposed event-triggered strategy.