A class of neural networks that solve linear programming problems is analyzed, The neural networks considered are modeled bq dynamic gradient systems that are constructed using a parametric family of exact (nondifferentiable) penalty functions. It is pro, ed 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.