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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.
Chong et al. (Fri,) studied this question.