Neural network design using linear programming and relaxation

Two new approaches to designing Hopfield neural networks using linear programming and relaxation are presented. These approaches are shown to be the natural ones given the form of the network dynamics. Computer simulations show that linear programming and relaxation are more effective than the sum of outer products rule in that they provide a larger capacity for the network. The new approaches are also shown to make the design process very flexible: they can guarantee that the given memories are all fixed points, they can incorporate a minimum radius of attraction, and they can accommodate restricted connectivities or regular network topologies. Statistical experiments are presented to illustrate these claims