LINEAR AND QUADRATIC-PROGRAMMING NEURAL NETWORK ANALYSIS

This paper presents an analysis of neural networks for linear and quadratic programming. The network proposed by Kennedy and Chua is justified from the viewpoint of optimization theory and the technique is extended to solve other optimization problems, such as the least-squares problem. For quadratic programming, the network converges either to an equilibrium or to an exact solution, depending on whether the problem has constraints or not. The results also suggest an analytical approach to solve the linear system Bx = b without calculating the matrix inverse. The results are directly applicable to optimization problems with C2 convex objective functions and linear constraints. The dynamics and applicability of the networks are demonstrated by simulation. The distance between the equilibria of the networks and the problem solutions can be controlled by the appropriate choice of a network parameter.