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A NEURAL NETWORK FOR THE GENERALIZED NONLINEAR COMPLEMENTARITY PROBLEM OVER A POLYHEDRAL CONE
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- Journal:
- Journal of the Australian Mathematical Society / Volume 99 / Issue 3 / December 2015
- Published online by Cambridge University Press:
- 30 October 2015, pp. 364-379
- Print publication:
- December 2015
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- Article
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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.
