Predefined-Time Convergence of Proximal Dynamics Methods for Equilibrium Problems*

In this paper, a predefined-time convergent proximal dynamics model (PDM) is proposed to address equilibrium problems (EPs). Firstly, two improved predefined-time convergence criterion of PDM are introduced by employing proximal operator, appropriate Lyapunov functions and the well-recognized comparison principle. Compared with previous results, a distinctive feature of our proposed predefined-Time convergence method for PDM is that it is independent of the initial conditions, system coefficients and step size, which ensures that the system converges to the equilibrium point in a predefined time. Moreover, the design optimized for predefined-time convergence avoid the delays associated with parameter tuning and condition adaptation in traditional approaches, thereby enhancing efficiency and practical applicability. Finally, numerical examples are provided to demonstrate the validity of the theory.