An Event-Triggered Approach for Gradient Tracking in Consensus-Based Distributed Optimization

This paper is concerned with a communication-efficient algorithm update scheme for solving distributed convex optimization problems by introducing a distributed event-triggered approach. Compared with real-time consensus-based distributed optimization algorithms in the literature, this paper focuses on extending the real-time gradient tracking scheme and proposes a novel distributed event-triggering condition to reduce the frequency of information exchange between agents in a network. The proposed event-triggered approach for consensus-based distributed optimization algorithms not only avoids the real-time consecutive communication and the coordinated computation between agents but reduces the computation load of algorithm execution. Furthermore, the proposed event-triggering condition depends on only local states from neighbors at only their event times and does not require a global and homogeneous sampling period. In addition, this paper analytically shows that the proposed consensus-based distributed optimization algorithm based on an event-triggered approach can also converge to the exact optimal solution with a linear convergence rate even if the real-time consecutive communication between agents is replaced with sporadic communication.