TY - JOUR
T1 - Solving nonlinear complementarity problems with neural networks
T2 - A reformulation method approach
AU - Liao, Li-Zhi
AU - Qi, Houduo
AU - Qi, Liqun
N1 - Funding Information:
This work is supported in part by grant FRG/97-98/II-42 of Hong Kong Baptist University and the Australian Research Council.
PY - 2001/6/1
Y1 - 2001/6/1
N2 - 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.
AB - 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.
KW - Neural network
KW - Nonlinear complementarity problem
KW - Stability
KW - Reformulation
UR - http://www.scopus.com/inward/record.url?scp=0035361448&partnerID=8YFLogxK
U2 - 10.1016/S0377-0427(00)00262-4
DO - 10.1016/S0377-0427(00)00262-4
M3 - Journal article
AN - SCOPUS:0035361448
SN - 0377-0427
VL - 131
SP - 343
EP - 359
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 1-2
ER -