Projection neural networks for solving constrained convex and degenerate quadratic problems

In this paper, we further analyze and prove the stability and convergence of the proposed dynamic system. We get that this network is complete stable, which can be used to solve an associated constrained convex optimization problem. Meanwhile, in order to show the wider domain of the method for stability used in this paper, we propose another neural network to solve a class of degenerate quadratic program. This network has a simpler structure than the other networks used to solve this class of problem. Furthermore, by introducing two new Lyapunov functions, we get that, for any initial points, all the obtained results in this paper remain valid, which improve the existing ones. Particularly, we also get some finite time convergence and exponential convergence results. Simulation examples show the correctness of the results in this paper and the effectiveness of the proposed neural networks to solve the two classes of optimization problems.