An Event-Based Delayed Projection Row-Stochastic Method for Distributed Constrained Optimization Over Time-Varying Graphs

This article investigates the distributed constrained optimization problem with event-triggered communication over time-varying weight-unbalanced directed graphs. A more generalized network model is considered where the communication topology may be variable and unbalanced over time, the information flows across agents are subject to time-varying communication delays, and agents are not required to know their out-degree information accurately. To address the above challenges, we propose a novel discrete-time distributed event-triggered delay subgradient algorithm. To facilitate convergence analysis, a consensus-only "virtual" agent technique is employed, dynamically adjusting its state (active or asleep) to ensure a delay-free information flow among agents. Additionally, an augmentation approach is proposed to ensure that the augmented time-varying weight matrix is row-stochastic. It is shown that the agents' local decision variables converge to the same optimal solution, in the case of reasonable communication delays and event-triggering thresholds. Numerical examples show the efficiency of the proposed algorithm.