Neurodynamics for Equality-Constrained Time-Variant Nonlinear Optimization Using Discretization

Time-variant problems are widespread in science and engineering, and discrete-time recurrent neurodynamics (DTRN) method has been proved to be an effective way to deal with a variety of discrete time-variant problems. However, this DTRN method is usually based on the study of continuous time-variant problems and lacks a direct study of discrete time-variant problems. To solve the abovementioned problem, based on a pioneering direct discretization technique, we study and develop a new DTRN method to solve equality-constrained discrete time-variant nonlinear optimization (EC-DTVNO) problem. Specifically, first, to solve the EC-DTVNO problem, the recent method widely used by researchers is Lagrange multiplier method. By introducing Lagrange multiplier to construct Lagrange function, the objective function and equality constraint are integrated into a discrete time-variant nonlinear system. Then, the corresponding error function is defined, and the corresponding DTRN method for solving the EC-DTVNO problem can be obtained by direct discretization technique. Thereafter, this DTRN method is analyzed theoretically and its convergence is proved. In addition, numerical experiments and application experiments further confirm the effectiveness and superiority of DTRN method.