An analysis of a class of neural networks for solving linear programming problems
Edwin K. P. Chong, Siqi Hui, Stanisław H. Żak · IEEE Transactions on Automatic Control · 1999
A class of neural networks that solve linear programming problems is analyzed. The neural networks considered are modeled by dynamic gradient systems that are constructed using a parametric family of exact (nondifferentiable) penalty functions. It is proved that for a given linear programming problem and sufficiently large penalty parameters, any trajectory of the neural network converges in finite time to its solution set. For the analysis, Lyapunov-type theorems are developed for finite time convergence of nonsmooth sliding mode dynamic systems to invariant sets. The results are illustrated via numerical simulation examples.