Advertisement

A Nonlinear Neural Network’s Stability Analysis and Its kWTA Application

  • Yinhui Yan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9377)

Abstract

In this paper, the stability of a novel nonlinear neural network solving linear programming problems is studied. We prove that this nonlinear neural network is stable in the sense of Lyapunov under certain conditions. Inspired by the study of this neural network, we propose a novel neural system to solving the k-winners-take-all (kWTA) problem. Numerical simulations demonstrate that the effectiveness and good performance of our new kWTA neural network.

Keywords

Nonlinear Neural Network Lyapunov Stability Linear Programming kWTA 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Dorfman, R., Samuelson, P.A. and Solow, R. M.: Linear Programming and Economic Analysis. Dover Publications (1987)Google Scholar
  2. 2.
    Matousek, J., Gärtner, B.: Understanding and Using Linear Programming. Springer (2006)Google Scholar
  3. 3.
    Gass, S.I.: Linear Programming: Methods and Applications, 5th edn. Dover Publications (2010)Google Scholar
  4. 4.
    Sultan, A.: Linear Programming: An Introduction With Applications, 2nd edn. CreateSpace Independent Publishing Platform (2011)Google Scholar
  5. 5.
    Tank, D.W., Hopfield, J.J.: Simple neural optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit. IEEE Transactions on Circuits and Systems 33(5), 533–541 (1986)CrossRefGoogle Scholar
  6. 6.
    Hopfield, J.J., Tank, D.W.: Computing with neural circuits: A model. Science 233, 625–633 (1986)CrossRefGoogle Scholar
  7. 7.
    Kennedy, M.P., Chua, L.O.: Neural networks for nonlinear programming. IEEE Transactions on Circuits and Systems 35(5), 554–562 (1988)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Maa, C.Y., Schanblatt, M.A.: A two-phase optimization neural network. IEEE Transactions on Neural Network 3(6), 1003–1009 (1992)CrossRefGoogle Scholar
  9. 9.
    Xia, Y.: A new neural network for solving linear programming problems and its application. IEEE Transactions on Neural Networks 7(2), 525–529 (1996)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Zhang, S., Constantinides, A.G.: Lagrange programming neural networks. IEEE Transactions on Circuits and Systems II 39(7), 441–452 (1992)CrossRefGoogle Scholar
  11. 11.
    Wang, J.: A deterministic annealing neural network for convex programming. Neural Networks 5(4), 962–971 (1994)MathSciNetGoogle Scholar
  12. 12.
    Nguyen, K.V.: A Nonlinear Neural Network for Solving Linear Programming Problems. In: International Symposium on Mathematical Programming, ISMP 2000, Atlanta, GA, USA (2000)Google Scholar
  13. 13.
    Suresh, S., Mani, V., Omkar, S.N., Kim, H.J.: Parallel Video Processing Using Divisible Load Scheduling Paradigm. Journal of Broadcast Engineering 10(1), 83–102 (2005)Google Scholar
  14. 14.
    Senthilnath, J., Omkar, S.N., Mani, V., Katti, A.R.: Cooperative communication of UAV to perform multi-task using nature inspired techniques. In: IEEE Symposium on Computational Intelligence for Security and Defense Applications (CISDA), pp. 45–50 (2013)Google Scholar
  15. 15.
    Yan, Y.: A New Nonlinear Neural Network for Solving QP Problems. In: Zeng, Z., Li, Y., King, I. (eds.) ISNN 2014. LNCS, vol. 8866, pp. 347–357. Springer, Heidelberg (2014)Google Scholar
  16. 16.
    Taylor, J.G.: Mathematical Approaches to Neural Networks. North-Holland (1993)Google Scholar
  17. 17.
    Harvey, R.L.: Neural Network Principles. Prentice Hall (1994)Google Scholar
  18. 18.
    Veelenturf, L.: Analysis and Applications of Artifical Neural Networks. Prentice Hall (1995)Google Scholar
  19. 19.
    Rojas, R., Feldman, J.: Neural Networks A Systematic Introduction. Springer (1996)Google Scholar
  20. 20.
    Mehrotra, K., Mohan, C.K., Ranka, S.: Elements of Artificial Neural Networks. MIT Press (1997)Google Scholar
  21. 21.
    Haykin, S.: Neural Networks A Comprehensive Foundation, 2nd edn. Prentice Hall (1998)Google Scholar
  22. 22.
    Michel, A., Liu, D.: Qualitative Analysis and Synthesis of Recurrent Neural Networks. CRC Press (2001)Google Scholar
  23. 23.
    Hagan, M.T., Demuth, H.B., Beale, M.H.: Neural Network Design. Martin Hagan (2002)Google Scholar
  24. 24.
    Gurney, K.: An Introduction to Neural Networks. CRC Press (2003)Google Scholar
  25. 25.
    Graupe, D.: Principles of Artificial Neural Networks, 2nd edn. World Scientific Pub. Co. Inc. (2007)Google Scholar
  26. 26.
    Krogh, A., Hertz, J., Palmer, R.G.: Introduction to the Theory of Neural Computation. Addison-Wesley, Redwook (1991)Google Scholar
  27. 27.
    Marr, D., Poggio, T.: Cooperative computation of stereo disparity. Science 195, 283–328 (1977)Google Scholar
  28. 28.
    Yuille, A.L., Geiger, D.: The Handbook of Brain Theory and Neural Networks. MIT Press (2002)Google Scholar
  29. 29.
    Xia, Y., Feng, G., Wang, J.: A primal-dual neural network for online resolving constrained kinematic redundancy in robot motion control. IEEE Transactions on Systems, Man and Cybernetics 35(1), 54–64 (2005)CrossRefGoogle Scholar
  30. 30.
    Xia, Y., Wang, J.: A general projection neural network for solving monotone variational inequalities and related optimization problems. IEEE Transactions on Neural Networks 15(2), 318–328 (2004)CrossRefGoogle Scholar
  31. 31.
    Gu, S., Wang, J.: A K-Winners-Take-All Neural Network Based on Linear Programming Formulation. In: Proceedings of International Joint Conference on Neural Networks, Orlando, Florida, USA (2007)Google Scholar
  32. 32.
    Boyd, S., Vandenbeghe, L.: Convex Optimization. Cambridge University Press (2004)Google Scholar
  33. 33.
    Bertsekas, D.P., Tsitsiklis, J.N.: Parallel and Distributed Computation: Numerical Methods. Prentice-Hall (1989)Google Scholar
  34. 34.
    Wang, J.: Analogue neural network for solving the assignment problem. Electronics Letters 28(11), 1047–1050 (1992)CrossRefGoogle Scholar
  35. 35.
    Hu, X., Wang, J.: Solving the assignment problem with the improved dual neural network. In: Liu, D., Zhang, H., Polycarpou, M., Alippi, C., He, H. (eds.) ISNN 2011, Part I. LNCS, vol. 6675, pp. 547–556. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  36. 36.
    Effati, S., Ranjbar, M.: Neural network models for solving the maximum flow problem. Applications and Applied Mathematics 3(3), 149–162 (2008)MathSciNetMATHGoogle Scholar
  37. 37.
    Nazemi, A., Omidi, F.: A capable neural network model for solving the maximum flow problem. Journal of Computational and Applied Mathematics 236(14), 3498–3513 (2012)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

<SimplePara><Emphasis Type="Bold">Open Access</Emphasis> This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 2.5 International License (http://creativecommons.org/licenses/by-nc/2.5/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made. </SimplePara> <SimplePara>The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.</SimplePara>

Authors and Affiliations

  1. 1.Shenzhen Airlines Co., Ltd.Shenzhen Bao’an International AirportShenzhenChina
  2. 2.College of Civil AviationNanjing University of Aeronautics and AstronauticsNanjingChina

Personalised recommendations