Gradient-Free Accelerated Event-Triggered Scheme for Constrained Network Optimization in Smart Grids

This paper proposes a novel projected primal-dual approach for a class of constrained network optimization problems in smart grids without explicit system models, aiming at improving system convergence rate and saving network resources simultaneously. Particularly, the primal step in the optimization procedure is updated without gradient information, by using the two-point zeroth-order optimization (ZO), and the dual step is iterated via real-time measurements, respectively. Then, an event-triggered mechanism (ETM) is designed for the dual variable as the coordination signal, with the hope of reducing the communication burden. Furthermore, extra momentum terms are incorporated to both primal and dual iterations to accelerate the convergence rate. By trading off the system performance and communication cost, it turns out that the convergence can be guaranteed under the specific stepsize condition and designed triggering threshold. Finally, two practical applications in smart grids are presented to verify the effectiveness of the proposed gradient-free control approach.