Predefined-time with time-varying coefficients neurodynamic for composite optimization problems

Abstract

In this paper, we propose a predefined-time with time-varying coefficients neurodynamic (PTTVCN) model to solve composite optimization problems (COPs). We first present the Lyapunov stability conditions for predefined-time stability in time-varying dynamical system and provide specific inferences under different time-varying coefficients. We then propose the PTTVCN model to solve COPs based on the predefined-time stability conditions of time-varying dynamical system. Theoretical analysis verifies that the PTTVCN model can achieve uniform convergence within predefined time and possesses a certain degree of noise resistance. Simulation results are given to show the effectiveness of the proposed predefined-time stability neurodynamic model with time-varying coefficients for COPs. Finally, numerical experiments on both image restoration and Poisson regression problems validate the superiority of the proposed method.