Primal–dual solution for the linear programming problems using neural networks

In this paper we represent two new methods for the solution of canonical form linear programming problems. In order to solve this linear programming problem we must minimize energy function of the corresponding neural network. Here energy function is considered as a Liapunov function and we use treated Hopfield neural network. First new method finds optimal solution for primal problem, using neural network, while second new method composes primal and dual problem and therefore finds optimal solution for both problems. Numerical results compared with simplex solution, and find that the convergence of two new methods to the correct solution is too fast, even faster than Neguyen's method. The new methods are fully stable.