The Study Of Solving Quadratic Program Problems By Neural Networks

In 1980s, Hopfield and Tank proposed a novel artificial neural network for solving linear programming problems. From then on, more and more attentions have been paid in research and application of such area. Comparing with traditional optimization algorithms, artificial neural network technique has more merits, such as faster convergence rate, hardware implementation and real-time control etc. In order to apply the artificial neural networks to solve optimization problems, it is required that the network is completely stable. Namely, output trajectories of neural networks converge to a stable equilibrium point or a stable equilibrium points set, and this equilibrium point is equivalent to the optimal solution of the optimization problem. In this paper, the methods of solving quadratic program problems by neural networks are studied. This paper is divided into five chapters:In Chapter 1, the background and developments of neural networks are introduced, and the existing work of solving optimization problems by neural networks is analysed.In Chapter 2, some theorems and lemmas in the optimization theory are introducd.In Chapter 3, solving interval quadratic program with box set constraints in engineering by interval projection neural network is discussed, and the existence, uniqueness and global exponential stability of the equilibrium point for the proposed neural network are analysed.In Chapter 4, solving the degenerate convex quadratic program problems by the projection neural network is studied, and the global convergence of the proposed neural network is proved.In Chapter 5, a neural network for solving a class of convex optimization problems with linear and nonlinear parametric constraints is constructed. In addition to, the global asymptotic stability of the proposed neural network is proved by using Lyapunov function method.