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

Volume

44

Issue

11

fYear

1999

fDate

11/1/1999 12:00:00 AM

Firstpage

1995

Lastpage

2006

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;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.802909

Filename

802909