A Novel Distributed Prescribed-Time Convergence Acceleration Algorithm with Time Rescaling

In this article, we present a novel distributed algorithm for prescribed-time convergence acceleration with time rescaling. Two novel prescribed-time acceleration algorithms are designed to tackle distributed unconstrained optimization problems and distributed optimization problems with constraints, effectively mirroring centralized optimization tasks within the framework of a closed convex set. We introduce several pivotal theorems, and the convergence of these algorithms are rigorously demonstrated through the application of Lyapunov functions. Finally, some comprehensive numerical simulations are conducted to validate the practicality and robustness of our theoretical findings.