Skip to main content
Log in

Indefinite quadratic fractional functional programming

  • Published:
Metrika Aims and scope Submit manuscript

Abstract

The present paper suggests a finite iteration technique for findinglocal minimum of a special type quasi-concave quadratic fractional functional subject to linear inequalities. The procedure adopted is exactly similar to “Simplex Technique” in linear programming and the problem has been attacked directly starting with a basic feasible solution and finding conditions under which the solution can be subjected to improvement. A numerical example has been given to illustrate the procedure.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Aggarwal, S. P.: “A Simplex Technique for a particular Convex Programming Problem”. Canadian Operational Research Soc. Jour. Vol. 4, No. 2, pp. 82–89, 1966.

    Google Scholar 

  • Bector, C. R.: “Programming problems with Convex Fractional Functions”. Opns. Res. (U.S.A.), Vol. 16, No. 2, 1968, pp. 383–391.

    MATH  MathSciNet  Google Scholar 

  • Candler, W. andR.J. Townsley: “The maximisation of a Quadratic function of variables subject to linear inequalities”. Management Science, Vol. 10, No. 3, 1964.

  • Charnes, A. andW. W. Cooper: “Programming with Linear Fractional Functionals”. Nav. Res. Log. Quart. Vol. 9, pp. 181–186 (Sept.–Dec. 1962).

    MATH  MathSciNet  Google Scholar 

  • Gass, S. I.: “Linear Programming”. McGraw-Hill, New York, 1958.

    MATH  Google Scholar 

  • Gupta, S. K. andC. R. Bector: “Nature of Quotients, Products and Rational Powers of Convex (concave — Like Functions”. The Mathematics Student (India), 1968, pp. 63–67.

  • Hadley, G.: “Linear Programming”. Reading Mass: Addison Wesley, 1962.

    MATH  Google Scholar 

  • Kanti, S.: “Quadratic Programming”. Cahiers du Centre d’Etudes de Recherche Operationelle, Vol. 8, No. 4, pp. 223–233, 1966.

    Google Scholar 

  • Mangasarian, O. L.: “Pseudo Convex Functions”. J. SIAM Control, Ser. A., Vol. 3, No. 2, pp. 281–290, 1965.

    Article  MathSciNet  MATH  Google Scholar 

  • Martos, B.: “The Direct Power of Adjacent Vertex Programming Methods”. Management Science, Vol. 12, No. 3, pp. 241–252, 1965.

    Article  MathSciNet  Google Scholar 

  • Ponstein, J.: “Seven kinds of Convexity”. SIAM Review, Vol. 9, No. 1, pp. 115–120, 1967.

    Article  MATH  MathSciNet  Google Scholar 

  • Rosen, J. B.: “The Gradient Projection Method for Non-linear Programming, Part I, Linear Constraints”. SIAM Jour. Vol. 8, pp. 181–217, 1960.

    MATH  Google Scholar 

  • —— “The Gradient Projection Method for Non-linear Programming, Part II, Non-linear Constraints”. SIAM Jour. Vol. 9, pp. 514–532, 1961.

    Google Scholar 

  • Zoutendijk, G.: “Maximising a Function in a Convex Region”. Jour. Roy. Stat. Soc. Ser. B. Vol. 21, pp. 338–355, 1959.

    MATH  MathSciNet  Google Scholar 

  • —— “Method of Feasible Directions”. Amsterdam: Elsevier, 1960.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bector, C.R. Indefinite quadratic fractional functional programming. Metrika 18, 21–30 (1972). https://doi.org/10.1007/BF02614233

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02614233

Keywords

Navigation