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Three Global Exponential Convergence Results of the GPNN for Solving Generalized Linear Variational Inequalities

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Advances in Neural Networks - ISNN 2008 (ISNN 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5263))

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Abstract

The general projection neural network (GPNN) is a versatile recurrent neural network model capable of solving a variety of optimization problems and variational inequalities. In a recent article [IEEE Trans. Neural Netw., 18(6), 1697-1708, 2007], the linear case of GPNN was studied extensively from the viewpoint of stability analysis, and it was utilized to solve the generalized linear variational inequality with various types of constraints. In the present paper we supplement three global exponential convergence results for the GPNN for solving these problems. The first one is different from those shown in the original article, and the other two are improved versions of two results in that article. The validity of the new results are demonstrated by numerical examples.

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References

  1. Hu, X., Wang, J.: Design of General Projection Neural Networks for Solving Monotone Linear Variational Inequalities and Linear and Quadratic Optimization Problems. IEEE Trans. Syst., Man, Cybern. B 37, 1414–1421 (2007)

    Article  Google Scholar 

  2. He, B.: Solution and Applications of a Class of General Linear Variational Inequalties. Sci. China Ser. A-Math. 39, 395–404 (1996)

    MATH  Google Scholar 

  3. Hu, X.: Applications of the General Projection Neural Network in Solving Extended Linear-Quadratic Programming Problems with Linear Constraints. Neurocomputing (accepted)

    Google Scholar 

  4. Gao, X.B.: A Neural Network for a Class of Extended Linear Variational Inequalities. Chinese Jounral of Electronics 10, 471–475 (2001)

    Google Scholar 

  5. Xia, Y., Wang, J.: A General Projection Neural Network for Solving Monotone Variational Inequalities and Related Optimization Problems. IEEE Trans. Neural Netw. 15, 318–328 (2004)

    Article  MathSciNet  Google Scholar 

  6. Hu, X., Wang, J.: Solving Generally Constrained Generalized Linear Variational Inequalities Using the General Projection Neural Networks. IEEE Trans. Neural Netw. 18, 1697–1708 (2007)

    Article  Google Scholar 

  7. Zeng, Z., Wang, J., Liao, X.: Global Exponential Stability of a General Class of Recurrent Neural Networks with Time-Varying Delays. IEEE Trans. Circuits Syst. I 50, 1353–1358 (2003)

    Article  MathSciNet  Google Scholar 

  8. Xia, Y., Feng, G., Kamel, M.: Development and Analysis of a Neural Dynamical Approach to Nonlinear Programming Problems. IEEE Trans. Automatic Control 52, 2154–2159 (2007)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. State Key Laboratory of Intelligent Technology and Systems, Tsinghua National Laboratory for Information Science and Technology (TNList), Department of Computer Science and Technology, Tsinghua University, Beijing, 100084, China

    Xiaolin Hu & Bo Zhang

  2. School of Automation, Wuhan University of Technology, Wuhan, 430070, China

    Zhigang Zeng

Authors
  1. Xiaolin Hu
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  2. Zhigang Zeng
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  3. Bo Zhang
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Technology, Tsinghu University, 100084, Beijing, China

    Fuchun Sun

  2. Institute TAMS (Technical Aspects of Multimodal Systems), department of Informatics, University of Hamburg, Vogt-Koelln-Straße 30, 22527, Hamburg, Germany

    Jianwei Zhang

  3. Intel China Research Center, 8/F, Peking University, Department of Machine Intelligence, 100871, Beijing, China

    Ying Tan

  4. Department of Mathematics, Southeast University, 210096, Nanjing, China

    Jinde Cao

  5. Departamento de Control Automático, CINVESTAV-IPN, A.P. 14-740, Av.IPN 2508, 07360, México D.F., México

    Wen Yu

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© 2008 Springer-Verlag Berlin Heidelberg

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Hu, X., Zeng, Z., Zhang, B. (2008). Three Global Exponential Convergence Results of the GPNN for Solving Generalized Linear Variational Inequalities. In: Sun, F., Zhang, J., Tan, Y., Cao, J., Yu, W. (eds) Advances in Neural Networks - ISNN 2008. ISNN 2008. Lecture Notes in Computer Science, vol 5263. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87732-5_35

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  • DOI: https://doi.org/10.1007/978-3-540-87732-5_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87731-8

  • Online ISBN: 978-3-540-87732-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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