TY - JOUR
T1 - A neural network for monotone variational inequalities with linear constraints
AU - Gao, Xing Bao
AU - LIAO, Lizhi
N1 - Funding Information:
The research was supported in part by grants FRG/99-00/II-23 and FRG/00-01/II-63 of Hong Kong Baptist University.
PY - 2003/1/27
Y1 - 2003/1/27
N2 - Variational inequality is a uniform approach for many important optimization and equilibrium problems. Based on the necessary and sufficient conditions for the solution, this Letter presents a neural network model for solving linearly constrained variational inequalities. Several sufficient conditions are provided to ensure the asymptotic stability of the proposing network. There is no need to estimate the Lipschitz constant, and no extra parameter is introduced. Since the sufficient conditions provided in this Letter can be easily checked in practice, these new results have both theoretical and application values. The validity and transient behavior of the proposing neural network are demonstrated by some numerical examples.
AB - Variational inequality is a uniform approach for many important optimization and equilibrium problems. Based on the necessary and sufficient conditions for the solution, this Letter presents a neural network model for solving linearly constrained variational inequalities. Several sufficient conditions are provided to ensure the asymptotic stability of the proposing network. There is no need to estimate the Lipschitz constant, and no extra parameter is introduced. Since the sufficient conditions provided in this Letter can be easily checked in practice, these new results have both theoretical and application values. The validity and transient behavior of the proposing neural network are demonstrated by some numerical examples.
KW - Convergence
KW - Neural network
KW - Stability
KW - Variational inequality
UR - http://www.scopus.com/inward/record.url?scp=0037467706&partnerID=8YFLogxK
U2 - 10.1016/S0375-9601(02)01673-0
DO - 10.1016/S0375-9601(02)01673-0
M3 - Article
AN - SCOPUS:0037467706
VL - 307
SP - 118
EP - 128
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
SN - 0375-9601
IS - 2-3
ER -