Advertisement

A neural network model for quadratic programming with simple upper and lower bounds and its application to linear programming

  • Xiang-sun Zhang
  • Hui-can Zhu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 834)

Abstract

In this paper we put forward a neural network model for quadratic programming problems with simple upper and lower bounds and analyze the properties of solutions obtained by the model. It is shown that linear programming problems can be transferred into such quadratic programming problems and be solved by the model.

Key words

neural network linear programming quadratic programming limit set 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Hopfield, J.J. & Tank, D.W., (1985). Neural computation of decision in optimization problems. Biological cybernetics, 52, 141–152.PubMedGoogle Scholar
  2. 2.
    Tank, D.W., & Hopfield, J.J., (1986). Simple neural optimization networks: An A/D converter, signal decision network and a linear programming circuit. IEEE transactions on circuit and systems, 33, 533–541.CrossRefGoogle Scholar
  3. 3.
    Kennedy, M.P., & Chua, L.O., (1988). Neural networks for nonlinear programming. IEEE transactions on circuit and systems, 35, 554–562.CrossRefGoogle Scholar
  4. 4.
    Bouzerdoum, A., & Pattison, T.R., (1993). Neural network for quadratic optimization with bound constraints. IEEE transactions on neural networks. 4, 293–304.CrossRefGoogle Scholar
  5. 5.
    Maa, C.Y., & Shanblatt, M.A., (1992). Linear and quadratic programming neural network analysis. IEEE transactions on neural networks, 3, 380–394.Google Scholar
  6. 6.
    Hopfield, J.J., Neurons with graded response have collective computational properties like those of two-state neurons. proceedings of natural academic science, USA, 81, 3088–3092.Google Scholar
  7. 7.
    Aiger, S.V.B., et al., (1990). A theoretical investigation into the performance of the Hopfield model. IEEE transactions on neural networks, 1, 204–215.CrossRefGoogle Scholar
  8. 8.
    Lasalle, (1976). the stability of dynamical systems. J.W.Arrowsmith Ltd.Google Scholar
  9. 9.
    Coste, J., et al., (1979). Simple kinetic model of symmetry breaking. Journal of statistical physics, 21, 33–50.Google Scholar
  10. 10.
    Arthur, R.M., (1969). Species packing and what interspecies competition minimizes. proceedings of natural academic science, USA, 64, 1369–1371.Google Scholar
  11. 11.
    Nemhauser, G.L., (1989). et al. Optimization. North-Holland.Google Scholar
  12. 12.
    Karmarkar, N., (1984). A new polynomial time algorithm for linear programming. Combinatoria, 4, 373–395.Google Scholar
  13. 13.
    Fletcher, (1980). Practical methods of optimization. Volume 1: Unconstrained optimization. John Wiley & Sons.Google Scholar
  14. 14.
    Gill, P., (1981). et al. Practical Optimization. Academic Press.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Xiang-sun Zhang
    • 1
  • Hui-can Zhu
    • 1
  1. 1.Institute of Applied MathematicsAcademia SinicaBeijingChina

Personalised recommendations