Convergence Analysis of Discrete Time RNNs for Linear Variational Inequality Problem

Huajin Tang; Kay Chen Tan; Zhang Yi

doi:10.1007/978-3-540-69226-3_6

Convergence Analysis of Discrete Time RNNs for Linear Variational Inequality Problem

Huajin Tang
, Kay Chen Tan
, Zhang Yi

Research output: Chapters, Conference Papers, Creative and Literary Works › Chapter in research book/monograph/textbook (Author) › peer-review

Abstract

In this chapter, we study the convergence of a class of discrete recurrent neural networks to solve Linear Variational Inequality Problems (LVIPs). LVIPs have important applications in engineering and economics. Not only the networks exponential convergence for the case of positive definite matrix is established, but its global convergence for positive semidefinite matrice is also proved. Conditions are derived to guarantee the convergences of the network. Comprehensive examples are discussed and simulated to illustrate the results.

Original language	English
Title of host publication	Neural Networks
Subtitle of host publication	Computational Models and Applications
Publisher	Springer Berlin Heidelberg
Chapter	6
Pages	81-97
ISBN (Electronic)	978-3-540-69226-3
ISBN (Print)	978-3-540-69225-6
DOIs	https://doi.org/10.1007/978-3-540-69226-3_6
Publication status	Published - 2007
Externally published	Yes

Publication series

Name	Studies in Computational Intelligence
Volume	53
ISSN (Print)	1860-949X
ISSN (Electronic)	1860-9503

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title = "Convergence Analysis of Discrete Time RNNs for Linear Variational Inequality Problem",

abstract = "In this chapter, we study the convergence of a class of discrete recurrent neural networks to solve Linear Variational Inequality Problems (LVIPs). LVIPs have important applications in engineering and economics. Not only the networks exponential convergence for the case of positive definite matrix is established, but its global convergence for positive semidefinite matrice is also proved. Conditions are derived to guarantee the convergences of the network. Comprehensive examples are discussed and simulated to illustrate the results.",

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Convergence Analysis of Discrete Time RNNs for Linear Variational Inequality Problem. / Tang, Huajin; Tan, Kay Chen; Yi, Zhang.
Neural Networks: Computational Models and Applications. Springer Berlin Heidelberg, 2007. p. 81-97 (Studies in Computational Intelligence; Vol. 53).

Research output: Chapters, Conference Papers, Creative and Literary Works › Chapter in research book/monograph/textbook (Author) › peer-review

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AU - Tan, Kay Chen

AU - Yi, Zhang

PY - 2007

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N2 - In this chapter, we study the convergence of a class of discrete recurrent neural networks to solve Linear Variational Inequality Problems (LVIPs). LVIPs have important applications in engineering and economics. Not only the networks exponential convergence for the case of positive definite matrix is established, but its global convergence for positive semidefinite matrice is also proved. Conditions are derived to guarantee the convergences of the network. Comprehensive examples are discussed and simulated to illustrate the results.

AB - In this chapter, we study the convergence of a class of discrete recurrent neural networks to solve Linear Variational Inequality Problems (LVIPs). LVIPs have important applications in engineering and economics. Not only the networks exponential convergence for the case of positive definite matrix is established, but its global convergence for positive semidefinite matrice is also proved. Conditions are derived to guarantee the convergences of the network. Comprehensive examples are discussed and simulated to illustrate the results.

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T3 - Studies in Computational Intelligence

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Convergence Analysis of Discrete Time RNNs for Linear Variational Inequality Problem

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