A neural network for a class of convex quadratic minimax problems with constraints

Xing Bao Gao; Lizhi LIAO; Weimin Xue

doi:10.1109/TNN.2004.824405

A neural network for a class of convex quadratic minimax problems with constraints

Xing Bao Gao, Lizhi LIAO^*, Weimin Xue

^*Corresponding author for this work

Department of Mathematics

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

43 Citations (Scopus)

Abstract

In this paper, we propose a neural network for solving a class of convex quadratic minimax problems with constraints. Four sufficient conditions are provided to ensure the asymptotic stability of the proposed network. Furthermore, the exponential stability of the proposing network is also proved under certain conditions. The results obtained here can be further extended to the globally projected dynamical system. In addition, some new stability conditions for the system are also obtained. Since our stability conditions can be easily checked in practice, these results becomes more attractive in real applications.

Original language	English
Pages (from-to)	622-628
Number of pages	7
Journal	IEEE Transactions on Neural Networks
Volume	15
Issue number	3
DOIs	https://doi.org/10.1109/TNN.2004.824405
Publication status	Published - May 2004

Scopus Subject Areas

Software
Computer Science Applications
Computer Networks and Communications
Artificial Intelligence

User-Defined Keywords

Convergence and stability
Minimax problem
Neural network
Saddle point

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10.1109/TNN.2004.824405

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title = "A neural network for a class of convex quadratic minimax problems with constraints",

abstract = "In this paper, we propose a neural network for solving a class of convex quadratic minimax problems with constraints. Four sufficient conditions are provided to ensure the asymptotic stability of the proposed network. Furthermore, the exponential stability of the proposing network is also proved under certain conditions. The results obtained here can be further extended to the globally projected dynamical system. In addition, some new stability conditions for the system are also obtained. Since our stability conditions can be easily checked in practice, these results becomes more attractive in real applications.",

keywords = "Convergence and stability, Minimax problem, Neural network, Saddle point",

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

note = "Funding Information: Manuscript received October 26, 2001; revised July 23, 2002 and October 23, 2002. This work was supported in part by Grants FRG/99-00/II-23 and FRG/00-01/II-63 of Hong Kong Baptist University and HKBU2059/02P from the Research Grant Council of Hong Kong. X.-B. Gao is with the Department of Mathematics, Shaanxi Normal University, Xi{\textquoteright}an, Shaanxi 710062, P. R. China. L.-Z. Liao and W. Xue are with the Department of Mathematics, Hong Kong Baptist University Kowloon Tong, Hong Kong, P.R. China (e-mail: liliao@hkbu.edu.hk; wmxue@hkbu.edu.hk). The corresponding author is L.-Z. Liao, Digital Object Identifier 10.1109/TNN.2004.824405",

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doi = "10.1109/TNN.2004.824405",

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T1 - A neural network for a class of convex quadratic minimax problems with constraints

AU - Gao, Xing Bao

AU - LIAO, Lizhi

AU - Xue, Weimin

N1 - Funding Information: Manuscript received October 26, 2001; revised July 23, 2002 and October 23, 2002. This work was supported in part by Grants FRG/99-00/II-23 and FRG/00-01/II-63 of Hong Kong Baptist University and HKBU2059/02P from the Research Grant Council of Hong Kong. X.-B. Gao is with the Department of Mathematics, Shaanxi Normal University, Xi’an, Shaanxi 710062, P. R. China. L.-Z. Liao and W. Xue are with the Department of Mathematics, Hong Kong Baptist University Kowloon Tong, Hong Kong, P.R. China (e-mail: liliao@hkbu.edu.hk; wmxue@hkbu.edu.hk). The corresponding author is L.-Z. Liao, Digital Object Identifier 10.1109/TNN.2004.824405

PY - 2004/5

Y1 - 2004/5

N2 - In this paper, we propose a neural network for solving a class of convex quadratic minimax problems with constraints. Four sufficient conditions are provided to ensure the asymptotic stability of the proposed network. Furthermore, the exponential stability of the proposing network is also proved under certain conditions. The results obtained here can be further extended to the globally projected dynamical system. In addition, some new stability conditions for the system are also obtained. Since our stability conditions can be easily checked in practice, these results becomes more attractive in real applications.

AB - In this paper, we propose a neural network for solving a class of convex quadratic minimax problems with constraints. Four sufficient conditions are provided to ensure the asymptotic stability of the proposed network. Furthermore, the exponential stability of the proposing network is also proved under certain conditions. The results obtained here can be further extended to the globally projected dynamical system. In addition, some new stability conditions for the system are also obtained. Since our stability conditions can be easily checked in practice, these results becomes more attractive in real applications.

KW - Convergence and stability

KW - Minimax problem

KW - Neural network

KW - Saddle point

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A neural network for a class of convex quadratic minimax problems with constraints

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