Fractional Order Iteration for Gradient Descent Method Based on Event-Triggered Mechanism

In this work, a novel gradient descent method based on event-triggered strategy has been proposed, which involves integer and fractional order iteration. Firstly, the convergence of integer order iterative optimization method and the stability of its associated system with integrator dynamics are linked. Based on this result, a fractional order iteration approach has been developed by modelling the system with fractional order dynamics. Secondly, to reduce the comsumption of computation, a feedback based event-triggered mechanism has been introduced to the gradient descent method. The convergence of this new event-triggered optimization algorithm is guaranteed by using a Lyapunov method, and Zeno behavior is proved to be avoided simultaneously. Lastly, the effectiveness and advantages of the proposed algorithms are verified by numerical simulations.