Advertisement

Differential Inclusions-Based Neural Networks for Nonsmooth Convex Optimization on a Closed Convex Subset

  • Shiji Song
  • Guocheng Li
  • Xiaohong Guan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3971)

Abstract

Differential inclusions-based dynamic feedback neural network models are introduced to solve in real time nonsmooth convex optimization problems restricted on a closed convex subset of R n . First,a differential inclusion-based dynamic feedback neural network model for solving unconstrained optimization problem is established, and its stability and convergence are investigated, then based on the preceding results and the method of successive approximation, differential inclusions-based dynamic feedback neural network models for solving in real time nonsmooth optimization problem on a closed convex subset are successively constructed, and its dynamical behavior and optimization capabilities are analyzed rigorously.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Hopfield, J.J., Tank, D.W.: Neural Computation of Decisions in Optimization Problems. Biol. Cybern. 52, 141–152 (1985)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Tank, D.W., Hopfield, J.J.: Simple Neural Optimization Network: An A/D Converter, Signal Decision Circuit, and a Linear Programming Circuit. IEEE Trans. Circuits Syst. 33, 533–541 (1986)CrossRefGoogle Scholar
  3. 3.
    Kennedy, M.P., Chua, L.O.: Neural Networks for Nonlinear Programming. IEEE Trans. Circuits Syst. 35, 554–562 (1988)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Rodríguez-Váquez, A., Rueda, R., Huertas, J.L., Sánchez-Sinencio, E.: Nonlinear Switched-Capacitor Neural Networks for Optimization Problems. IEEE Trans. Circuits Syst. 37, 384–397 (1990)CrossRefGoogle Scholar
  5. 5.
    Bouzerdoum, A., Pattison, T.R.: Neural Network for Quadratic Optimization with Bound Constraints. IEEE Trans. Neural Networks 4, 293–304 (1993)CrossRefGoogle Scholar
  6. 6.
    Sudharsanan, S., Sundareshan, M.: Exponential Stability and a Systematic Synthesis of a Neural Network for Quadratic Minimization. Neural Networks 4, 599–613 (1991)CrossRefGoogle Scholar
  7. 7.
    Leung, Y., Chen, K.Z., Gao, X.B.: A High-Performance Feedback Neural Network for Solving Convex Nonlinear Programming Problems. IEEE Trans. Neural Networks 14, 1469–1477 (2003)CrossRefGoogle Scholar
  8. 8.
    Forti, M., Nistri, P.: Global Convergence of Neural Networks with Discontinuous Neuron Activations. IEEE Trans.Circuits and Systems-I 50, 1421–1435 (2003)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Lu, W., Chen, T.: Dynamical Behaviors of Cohen-Grossberg Neural Networks with Discontinuous Activation Functions. Neural Networks 18, 231–242 (2005)zbMATHCrossRefGoogle Scholar
  10. 10.
    Forti, M., Nistri, P., Quincampoix, M.: Generalized Neural Network for Nonsmooth Nonlinear Programming Problems. IEEE Trans.Circuits and Systems-I 51, 1741–1754 (2004)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Aubin, J.P., Cellina, A.: Differential Inclusions. Springer, Berlin (1984)zbMATHGoogle Scholar
  12. 12.
    Dimitri, P.B.: Nonlinear Programming, 2nd edn. Athena Scientific, Belmont (1999)zbMATHGoogle Scholar
  13. 13.
    Filippov, A.F.: Differential Equations with Discontinuous Righthand Sides. Kluwer Academic, Dordrecht (1988)Google Scholar
  14. 14.
    Li, G., Song, S., Wu, C.: Subgradient-Based Feedback Neural Networks for Nondifferentiable Convex Optimization Problems. Science in China, Series F 49, 91–106 (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Shiji Song
    • 1
  • Guocheng Li
    • 1
  • Xiaohong Guan
    • 1
  1. 1.Department of AutomationTsinghua UniversityBeijingChina

Personalised recommendations