A Linear Algorithm for Quantized Event-Triggered Optimization Over Directed Networks

Dear Editor, This letter investigates a class of distributed optimization problems with constrained communication. A quantized discrete-time event-triggered zero-gradient-sum algorithm (QDE-ZGS) is developed to optimize the sum of local functions over weight-balanced directed networks. Based on an encoder-decoder scheme and a zooming-in technique, an event-triggered quantization communication is designed. Theoretical analysis shows that the exact convergence to the global optimal solution is guaranteed when the triggering threshold is bounded and the scaled sequence introduced by the zooming-in technique is quadratic summable. When the scaled sequence is bounded by an exponential decay function, QDE-ZGS converges linearly to the unique global optimal solution. Numerical simulations are conducted to demonstrate the theoretical results.