The University of Southampton
University of Southampton Institutional Repository

Solving nonlinear complementarity problems with neural networks: a reformulation method approach

Solving nonlinear complementarity problems with neural networks: a reformulation method approach
Solving nonlinear complementarity problems with neural networks: a reformulation method approach
In this paper, we present a neural network approach for solving nonlinear complementarity problems. The neural network model is derived from an unconstrained minimization reformulation of the complementarity problem. The existence and the convergence of the trajectory of the neural network are addressed in detail. In addition, we also explore the stability properties, such as the stability in the sense of Lyapunov, the asymptotic stability and the exponential stability, for the neural network model. The theory developed here is also valid for neural network models derived from a number of reformulation methods for nonlinear complementarity problems. Simulation results are also reported.
neural network, nonlinear complementarity problem, stability, reformulation
0377-0427
343-359
Liao, Li-Zhi
c79b29f2-ea1e-4e0e-badc-756956646ee1
Qi, Houduo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Qi, Liqun
69936be7-f1aa-4c1f-b403-5bd5f3ba7d4c
Liao, Li-Zhi
c79b29f2-ea1e-4e0e-badc-756956646ee1
Qi, Houduo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Qi, Liqun
69936be7-f1aa-4c1f-b403-5bd5f3ba7d4c

Liao, Li-Zhi, Qi, Houduo and Qi, Liqun (2001) Solving nonlinear complementarity problems with neural networks: a reformulation method approach. Journal of Computational and Applied Mathematics, 131 (1-2), 343-359. (doi:10.1016/S0377-0427(00)00262-4).

Record type: Article

Abstract

In this paper, we present a neural network approach for solving nonlinear complementarity problems. The neural network model is derived from an unconstrained minimization reformulation of the complementarity problem. The existence and the convergence of the trajectory of the neural network are addressed in detail. In addition, we also explore the stability properties, such as the stability in the sense of Lyapunov, the asymptotic stability and the exponential stability, for the neural network model. The theory developed here is also valid for neural network models derived from a number of reformulation methods for nonlinear complementarity problems. Simulation results are also reported.

This record has no associated files available for download.

More information

Published date: 2001
Keywords: neural network, nonlinear complementarity problem, stability, reformulation
Organisations: Operational Research

Identifiers

Local EPrints ID: 29637
URI: http://eprints.soton.ac.uk/id/eprint/29637
ISSN: 0377-0427
PURE UUID: b6ab1f00-b529-4c99-8c38-e3646cf1974a
ORCID for Houduo Qi: ORCID iD orcid.org/0000-0003-3481-4814

Catalogue record

Date deposited: 11 May 2006
Last modified: 16 Mar 2024 03:41

Export record

Altmetrics

Contributors

Author: Li-Zhi Liao
Author: Houduo Qi ORCID iD
Author: Liqun Qi

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×