A neural network for solving optimization problems with linear equality constraints

It is shown that Hopfield-like neural networks can compute good solutions to complex optimization problems. One difficulty of this approach is the selection of an energy function, particularly for the problems with constraints. Adding a `constraint violation penalty´ term to the energy function sometimes causes undesired local minimums corresponding to invalid solutions. A novel approach to the derivation of a neural network is introduced. This approach can always obtain valid solutions for problems with linear equality constraints. Instead of using penalty, a projection factor is incorporated in the neural network synthesis so that the convergence trace will stay in the constraint plan, and thus always return a valid solution