Discrete Time-Varying Equality Constrained Optimization: A Zeroing Neural Dynamic Method with Two Parameters

In this paper, the discrete time-varying equality constrained optimization (D-TV-ECO) problem based on discrete-time zeroing neural dynamic (DT-ZND) method is studied. Firstly, a continuous time-varying equality constrained optimization (C-TV-ECO) problem is presented. Secondly, the Lagrange function is constructed by introducing the Lagrange method, which integrates the objective function and related constraints into a continuous time-varying system. Then, a continuous-time ZND (CT-ZND) method is built. Afterward, using the discretization derivation method based on the expansion of four-step ZeaD formula (FsZF), a FsZF DT-ZND method for D-TV-ECO problem is proposed, which has two design parameters, including discretization parameter and convergence parameter. Significantly, the truncation error of the FsZF DT-ZND method has been elevated to the fourth-order, thereby enhancing the precision of the calculations. Theoretical analysis indicates that the FsZF DT-ZND method exhibits convergence and stability. In the numerical experiments, the impact of different values of the discretization parameter α and convergence parameter κ is analyzed. Finally, simulation experiments are conducted to further demonstrate the effectiveness and superiority of the FsZF DT-ZND method.