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 -