Title :
An analysis of a class of neural networks for solving linear programming problems
Author :
Chong, Edwin K P ; Hui, Stefen ; Zak, Stanislaw H.
Author_Institution :
Sch. of Electr. & Comput. Eng., Purdue Univ., West Lafayette, IN, USA
fDate :
11/1/1999 12:00:00 AM
Abstract :
A class of neural networks that solve linear programming problems is analyzed. The neural networks considered are modeled by dynamic gradient systems that are constructed using a parametric family of exact (nondifferentiable) penalty functions. It is proved that for a given linear programming problem and sufficiently large penalty parameters, any trajectory of the neural network converges in finite time to its solution set. For the analysis, Lyapunov-type theorems are developed for finite time convergence of nonsmooth sliding mode dynamic systems to invariant sets. The results are illustrated via numerical simulation examples
Keywords :
Lyapunov methods; convergence; linear programming; mathematics computing; neural nets; problem solving; Lyapunov-type theorems; convergence; dynamic gradient systems; invariant sets; linear programming problem solving; neural networks; nonsmooth sliding mode dynamic systems; numerical simulation; penalty functions; Constraint optimization; Control system analysis; Control systems; Differential equations; Failure analysis; Intelligent networks; Linear programming; Neural networks; Numerical simulation; Sliding mode control;
Journal_Title :
Automatic Control, IEEE Transactions on
