A capable neural network model for solving the maximum flow problem
Journal of Computational and Applied Mathematics
A neural network for the linear complementarity problem
Mathematical and Computer Modelling: An International Journal
An application of a merit function for solving convex programming problems
Computers and Industrial Engineering
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Neural networks for linear and quadratic programming are analyzed. The network proposed by M.P. Kennedy and L.O. Chua (IEEE Trans. Circuits Syst., vol.35, pp.554-562, May 1988) is justified from the viewpoint of optimization theory and the technique is extended to solve 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