Accelerating Fixed-Time Event-Triggered Optimization in Continuous and Discrete Time via Time-Varying Dynamical Systems.

This article proposes a fixed-time protocol for distributed optimization over multiagent systems (MASs), coupling time-varying dynamics with event-triggered communication. Unlike conventional constant-coefficient methods, our two-stage design guarantees fixed-time convergence independent of initial conditions, accelerates it via time-varying gain, and reduces overhead via dynamic triggering. The framework also extends to discrete-time settings, where a power-law decaying step-size yields phased convergence, fast contraction then fine-tuning, while retaining event-triggered savings. Rigorous analysis precludes Zeno and ensures robustness against bounded disturbances. Numerical experiments show 778% faster convergence and up to 10.34% overhead reduction over the best constant-gain baseline, while the discrete-time extension maintains savings over all admissible step sizes.