A neural network based on the generalized Fischer-Burmeister function for nonlinear complementarity problems

Jein-Shan Chen, Chun Hsu Ko, Shaohua Pan

Research output: Contribution to journalArticle

27 Citations (Scopus)

Abstract

In this paper, we consider a neural network model for solving the nonlinear complementarity problem (NCP). The neural network is derived from an equivalent unconstrained minimization reformulation of the NCP, which is based on the generalized Fischer-Burmeister function φ{symbol}p (a, b) = {norm of matrix} (a, b) {norm of matrix}p - (a + b). We establish the existence and the convergence of the trajectory of the neural network, and study its Lyapunov stability, asymptotic stability as well as exponential stability. It was found that a larger p leads to a better convergence rate of the trajectory. Numerical simulations verify the obtained theoretical results.

Original languageEnglish
Pages (from-to)697-711
Number of pages15
JournalInformation Sciences
Volume180
Issue number5
DOIs
Publication statusPublished - 2010 Mar 1

Fingerprint

Nonlinear Complementarity Problem
Norm of a matrix
Neural Networks
Trajectory
Asymptotic stability
Neural networks
Unconstrained Minimization
Lyapunov Stability
Exponential Stability
Reformulation
Trajectories
Neural Network Model
Asymptotic Stability
Rate of Convergence
Verify
Norm
Numerical Simulation
Computer simulation
Nonlinear complementarity problem

Keywords

  • Exponentially convergent
  • Generalized Fischer-Burmeister function
  • Neural network
  • The nonlinear complementarity problem

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Theoretical Computer Science
  • Computer Science Applications
  • Information Systems and Management

Cite this

A neural network based on the generalized Fischer-Burmeister function for nonlinear complementarity problems. / Chen, Jein-Shan; Ko, Chun Hsu; Pan, Shaohua.

In: Information Sciences, Vol. 180, No. 5, 01.03.2010, p. 697-711.

Research output: Contribution to journalArticle

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