A neural network for monotone variational inequalities with linear constraints

Xing Bao Gao; Lizhi LIAO

doi:10.1016/S0375-9601(02)01673-0

A neural network for monotone variational inequalities with linear constraints

Xing Bao Gao, Lizhi LIAO^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

20 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	118-128
Number of pages	11
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	307
Issue number	2-3
DOIs	https://doi.org/10.1016/S0375-9601(02)01673-0
Publication status	Published - 27 Jan 2003

Scopus Subject Areas

Physics and Astronomy(all)

User-Defined Keywords

Convergence
Neural network
Stability
Variational inequality

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10.1016/S0375-9601(02)01673-0

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title = "A neural network for monotone variational inequalities with linear constraints",

abstract = "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.",

keywords = "Convergence, Neural network, Stability, Variational inequality",

author = "Gao, {Xing Bao} and Lizhi LIAO",

note = "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. ",

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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

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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 -

A neural network for monotone variational inequalities with linear constraints

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