Development and Analysis of a Neural Dynamical Approach to Nonlinear Programming Problems

This technical note develops a neural dynamical approach to nonlinear programming (NP) problems, whose equilibrium points coincide with Karush-Kuhn-Tucker points of the NP problem. A rigorous analysis on the global convergence and the convergence rate of the proposed neural dynamical approach is carried out under the condition that the associated Lagrangian function is convex. Analysis results show that the proposed neural dynamical approach can solve general convex programming problems and a class of nonconvex programming problems. Two nonconvex programming examples are provided to demonstrate the performance of the developed neural dynamical approach.