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Keywords:
gradient tracking; event-triggered mechanism; multi-agent systems; distributed optimization
gradient tracking; event-triggered mechanism; multi-agent systems; distributed optimization
Summary:
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.
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