An analysis of a class of neural networks for solving linear programming problems

被引：98

作者：

Chong, EKP ^{[1
]}

Hui, S

Zak, SH

机构：

[1] Purdue Univ, Sch Elect & Comp Engn, W Lafayette, IN 47907 USA

[2] San Diego State Univ, Dept Math Sci, San Diego, CA 92182 USA

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 1999年 / 44卷 / 11期

基金：

美国国家科学基金会;

关键词：

invariant sets; linear programming; neural networks; nondifferentiable optimization; penalty functions; sliding modes;

D O I：

10.1109/9.802909

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

A class of neural networks that solve linear programming problems is analyzed, The neural networks considered are modeled bq dynamic gradient systems that are constructed using a parametric family of exact (nondifferentiable) penalty functions. It is pro, ed 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.

引用

页码：1995 / 2006

页数：12

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