The Projection Neural Network For Solving Interval Optimization Problem And Support Vector Classification

Neural network imitates the structure of the nerve cells of person, it takes one kind of non-linear auto-adapted dynamics system which is connected by a lot of complicated and orderly neurons.Now it has been used widely in many fields,such as: automatic control, combinatorial optimization, pattern recog- nition and image processing, robot control, signal transmission and so on.In the paper,we use the duality thorems of the optimization theory to let a kind of optimization problem in support vector machine (SVM) and interval quadratic programming problems transforme into its corresponding dual problem,using the KKT conditions, let the optimization dual problem transforme into the problem of the projection equations, using differential equation to build projection neural networks,let the equilibrium point of network be equivalent to the optimal solution of the optimization problem, through building a corresponding Lyapunov function ,the existence of the equilibrium point of network, uniqueness and global exponential stability conditions, thus we can solve the problem. Finally,there are several examples of simulation,they show the validity and the correctness of the conditions. Main content as follows:First of all, we introduce the research background and developments of neural networks. Besides, we show that it is necessary to investigate the stability of optimization neural networks.Secondly, in order to present the neural network for solving program -ming problems, we introduce the basic theory on the optimization problem.Thirdly, we solve the interval quadratic programming problem with the projection neural network.The existence of the equilibrium point of net- work and uniqueness and global exponential stability conditions is analyzed.Fourthly, for a class of support vector machine ,we use the projection neural network solve the problem, we can prove the the equilibrium point of network is equal to the optimal solution of the problem, and the global stability of the equilibrium network is analyzed.At last a summary of the paper is given, and the future research directions are forecasted.