In this paper we show that two ellipsoid algorithms can be used to tra
in single-layer neural networks with general staircase nonlinearities.
The ellipsoid algorithms have several advantages over other conventio
nal training approaches including (1) explicit convergence results and
automatic determination of linear separability, (2) an elimination of
problems with picking initial values for the weights, (3) guarantees
that the trained weights are in some ''acceptable region,'' (4) certai
n ''robustness'' characteristics, and (5) a training approach for neur
al networks with a wider variety of activation functions. We illustrat
e the training approach by training the MAJ function and then by showi
ng how to train a controller for a reaction chamber temperature contro
l problem.