On solving systems of linear inequalities with artificial neuralnetworks

The implementation of the relaxation-projection algorithm by artificial neural networks to solve sets of linear inequalities is examined. The different versions of this algorithm are described, and theoretical convergence results are given. The best known analog optimization solvers are shown to use the simultaneous projection version of it. Neural networks that implement each version are described. The results of tests, made with simulated realizations of these networks, are reported. These tests consisted in having all networks solve some sample problems. The results obtained help determine good values for the step size parameters, and point out the relative merits of the different networks.