A Recurrent Neural Network for Solving Bilevel Linear Programming Problem

Author

Xing He ; Chuandong Li ; Tingwen Huang ; Chaojie Li ; Junjian Huang

Author_Institution

Sch. of Electron. & Inf. Eng., Southwest Univ., Chongqing, China

Volume

25

Issue

4

fYear

2014

fDate

Apr-14

Firstpage

824

Lastpage

830

Abstract

In this brief, based on the method of penalty functions, a recurrent neural network (NN) modeled by means of a differential inclusion is proposed for solving the bilevel linear programming problem (BLPP). Compared with the existing NNs for BLPP, the model has the least number of state variables and simple structure. Using nonsmooth analysis, the theory of differential inclusions, and Lyapunov-like method, the equilibrium point sequence of the proposed NNs can approximately converge to an optimal solution of BLPP under certain conditions. Finally, the numerical simulations of a supply chain distribution model have shown excellent performance of the proposed recurrent NNs.

Keywords

Lyapunov methods; linear programming; numerical analysis; recurrent neural nets; BLPP; Lyapunov-like method; bilevel linear programming problem; differential inclusion; equilibrium point sequence; nonsmooth analysis; numerical simulation; optimal solution; penalty functions; recurrent NN; recurrent neural network; state variables; supply chain distribution model; Artificial neural networks; Educational institutions; Linear programming; Programming profession; Recurrent neural networks; Bilevel linear programming problem (BLPP); differential inclusions; nonsmooth analysis; recurrent neural network (NN);

fLanguage

English

Journal_Title

Neural Networks and Learning Systems, IEEE Transactions on

Publisher

ieee

ISSN

2162-237X

Type

jour

DOI

10.1109/TNNLS.2013.2280905

Filename

6606815