ET-DMGing: Event-triggered distributed momentum-gradient tracking optimization algorithm for multi-agent systems

This paper proposes an event-triggered distributed momentum-gradient tracking optimization algorithm (ET-DMGing) for the collaborative optimization problem of minimizing the sum of all agents' local objective functions in multi-agent systems.Firstly, gradient tracking is employed to precisely track the average momentum gradient for updating agent states, which effectively reduces their dwell time in flat and oscillatory regions.The proposed ET-DMGing exhibits enhanced directional consistency and dynamic stability during optimization by leveraging momentum accumulation effects, achieving a linear convergence rate.Secondly, a new event-triggered condition is proposed, which considers the dual metrics of state error and momentum gradient error.This allows for a more comprehensive assessment of the agents' triggering needs, avoiding instability caused by single-dimensional triggering, and improving the triggering threshold.This event-triggered condition reduces the communication frequency among agents.Thirdly, we rigorously proved that the proposed ET-DMGing converges to the global optimum at a linear convergence rate by employing the small-gain theorem.Furthermore, explicit convergence conditions have been derived for parameter selection, including step size parameters and event-triggered weighting coefficients.Finally, numerical simulations are performed to verify the effectiveness and accuracy of the theoretical results.