Numerical solutions for constrained quadratic problems using high-performance neural networks

Two new classes of neural networks for solving constrained quadratic programming problems are presented. The main advantage of these networks is the requirement to use economic analog multipliers for variables. The numerical simulations demonstrate that in the new neural networks not only the cost of the hardware implementation is not relatively expensive, but also accuracy of the solution is very good. The network dynamic behaviors are discussed. The numerical simulations show that an optimal solution of the quadratic problems is an equilibrium point of the neural dynamics, and vice versa. We show that these networks find the solution of both primal and dual problems, and converge to the corresponding exact solutions globally. The proposed new neural networks models are fully stable.