Distributed momentum gradient descent convex optimization algorithm with network communication

This paper proposes a distributed continuous-time momentum gradient descent (MGD) algorithm for convex optimization over multi-agent networks, where agents collaboratively minimize the sum of local convex cost functions through coordinated communication. First, we establish exponential convergence under ideal continuous-time coordination through Lyapunov analysis. To bridge the gap between theoretical designs and digital implementations, two strategies are developed: (1) a time-triggered control (TTC) scheme that guarantees stability under bounded sampling intervals; (2) a periodic event-triggered control (PETC) strategy. Notably, the PETC strategy is introduced to address the inefficiency in network resource utilization inherent in TTC by activating communication only when necessary. By formulating the PETC-based algorithm as a hybrid dynamical system with event-driven thresholds, we subsequently construct a parameterized hybrid Lyapunov function to rigorously prove the global asymptotic stability of the equilibrium point. Comprehensive numerical experiments confirm the convergence of the algorithm under both strategies, with PETC achieving a reduction in communication frequency compared to TTC, while maintaining solution accuracy.