Neural network models for Linear Programming
J.C. Culioli, Vladimir A. Protopopescu, C. Britton, N. Ericson · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 1989
The purpose of this paper is to present a neural network that solves the general Linear Programming (LP) problem. In the first part, we recall Hopfield and Tank's circuit for LP and show that although it converges to stable states, it does not, in general, yield admissible solutions. This is due to the penalization treatment of the constraints. In the second part, we propose an approach based on Lagragrange multipliers that converges to primal and dual admissible solutions. We also show that the duality gap (measuring the optimality) can be rendered, in principle, as small as needed. 11 refs.