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A NEURAL NETWORK FOR THE GENERALIZED NONLINEAR COMPLEMENTARITY PROBLEM OVER A POLYHEDRAL CONE

Published online by Cambridge University Press:  30 October 2015

YIFEN KE  and
CHANGFENG MA
YIFEN KE
Affiliation:
School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350117, PR China email yfke89@163.com
CHANGFENG MA*
Affiliation:
School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350117, PR China email macf@fjnu.edu.cn
*
✉macf@fjnu.edu.cn
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Abstract

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In this paper, we consider a neural network model for solving the generalized nonlinear complementarity problem (denoted by GNCP) over a polyhedral cone. The neural network is derived from an equivalent unconstrained minimization reformulation of the GNCP, which is based on the penalized Fischer–Burmeister function ${\it\phi}_{{\it\mu}}(a,b)={\it\mu}{\it\phi}_{\mathit{FB}}(a,b)+(1-{\it\mu})a_{+}b_{+}$. We establish the existence and the convergence of the trajectory of the neural network, and study its Lyapunov stability, asymptotic stability and exponential stability. It is found that a larger ${\it\mu}$ leads to a better convergence rate of the trajectory. Simulation results are also reported.

Keywords

generalized nonlinear complementarity problempolyhedral coneneural networkconvergence analysissimulation results

MSC classification

Primary: 90C33: Complementarity and equilibrium problems and variational inequalities (finite dimensions)
Secondary: 65K10: Optimization and variational techniques
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 99 , Issue 3 , December 2015 , pp. 364 - 379
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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