Proximal Dynamic Method With Time-Varying Coefficients for Equilibrium Problems: Fixed-Time Convergence

In this letter, a proximal dynamical system with time-varying coefficients for fixed-time (FXT) convergence is proposed to deal with the equilibrium problems (EPs). Initially, considering the non-smooth problem in optimization, we introduced the proximal dynamical system with FXT convergence. Compared with the finite-time (FT) convergence method, the convergence time of our algorithm is independent of the initial state, which enhances the robustness and ensures a fast convergence of the optimization process. Building on this foundation, the FXT convergence of the proximal dynamical system with time-varying coefficients is further investigated to realize the flexible adjustment of parameters, aiming at accelerating the convergence speed, reducing the oscillations and the process is not affected by the initial state. Ultimately, the efficacy of the proposed methods is validated through numerical experimentation.