Skip to main content
SpringerLink
Log in

On Linear Fractional Programming Problem and its Computation Using a Neural Network Model

  • Published:
Journal of Mathematical Modelling and Algorithms

Abstract

In this paper we consider linear fractional programming problem and look at its linear complementarity formulation. In the literature, uniqueness of solution of a linear fractional programming problem is characterized through strong quasiconvexity. We present another characterization of uniqueness through complementarity approach and show that the solution set of a fractional programming problem is convex. Finally we formulate the complementarity condition as a set of dynamical equations and prove certain results involving the neural network model. A computational experience is also reported.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Tank, D.W., Hopfield, J.J.: Simple neural optimization networks: an A/D converter, signal decision network, and a linear programming circuit. IEEE Trans. Circuits Systs. 33, 533–541 (1986)

    Article  Google Scholar 

  2. Kennedy, M.P., Chua, L.O.: Neural networks for non-linear programming. IEEE Trans. Circuits Systs. 35, 554–562 (1988)

    Article  MathSciNet  Google Scholar 

  3. Bazaraa, M.S., Sherali, H.D., Shetty, C.M.: Nonlinear Programming, Theory and Algorithms. Wiley, New York (1979)

    MATH  Google Scholar 

  4. Bajalinov, E.B.: Linear-fractional Programming: Theory, Methods, Applications and Software. Kluwer, USA (2003)

    MATH  Google Scholar 

  5. Charnes, A., Cooper, W.W.: Programming with linear fractional functionals. Nav. Res. Logist. Q. 9, 181–186 (1962)

    Article  MATH  MathSciNet  Google Scholar 

  6. Cottle, R.W., Pang, J.S., Stone, R.E.: The Linear Complementarity Problem. Academic, Boston (1992)

    MATH  Google Scholar 

  7. Xia, Y., Wang, J.: A recurrent neural network for solving linear projection equations. Neural Netw. 13, 337–350 (2000)

    Article  Google Scholar 

  8. Lemke, C.E.: Bimatrix equilibrium points and mathematical programming. Manage. Sci. 11, 681–689 (1965)

    MathSciNet  Google Scholar 

  9. Lemke, C.E., Howson, Jr. J.T.: Equilibrium points of bimatrix games. SIAM J. Appl. Math. 12, 413–423 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  10. Mohan, S.R.: The linear complementarity problem with a Z-matrix. Ph.D. thesis, Indian Statistical Institute, Calcutta (1976)

  11. Murty, K.G.: Linear Complementarity, Linear and Nonlinear Programming. Heldermann Verlag, Berlin (1988)

    MATH  Google Scholar 

  12. Schaible, S.: Fractional programming in handbook on global optimization. In: Horst, R., Pardalos, P.M. (eds.), pp. 495–608. Kluwer, Dordrecht (1995)

  13. Swarup, K.: Some aspects of linear fractional functionals programming. Aust. J. Stat. 7(3), 90–104 (1965)

    MATH  MathSciNet  Google Scholar 

  14. Swarup, K.: Linear fractional functionals programming. Oper. Res. 13, 1029–1036 (1965)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Indian Statistical Institute, New Delhi, 110 016, India

    S. K. Neogy

  2. Indian Statistical Institute, Kolkata, 700 108, India

    A. K. Das & P. Das

Authors
  1. S. K. Neogy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. K. Das
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. Das
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. K. Neogy.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Neogy, S.K., Das, A.K. & Das, P. On Linear Fractional Programming Problem and its Computation Using a Neural Network Model. J Math Model Algor 6, 577–590 (2007). https://doi.org/10.1007/s10852-007-9068-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10852-007-9068-3

Keywords

Mathematics Subject Classifications (2000)

Search

Navigation