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Duality in fractional programming

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Summary

In this paper, a dual problem to linear fractional functionals programming i. e.

$$\begin{gathered} Maximise Z = \frac{{c'x}}{{d'x}} \hfill \\ subject to Ax = b \hfill \\ x \geqslant 0 \hfill \\ \end{gathered} $$

is formulated. Certain duality theorems regarding the relationship between primal and dual problems are established.

Zusammenfassung

Es wird zu dem Programm mit gebrochen-linearer Zielfunktion:

$$\begin{gathered} Ax = b, x \geqslant 0 \hfill \\ Z = \frac{{c'x}}{{d'x}} \Rightarrow Max! \hfill \\ \end{gathered} $$

ein duales Programm aufgestellt. Gewisse Dualitätssätze über den Zusammenhang zwischen dem Primal- und Dualproblem werden aufgestellt.

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References

  1. Charnes, A. andW. W. Cooper: Programming with linear fractional functionals. — Nav. Res. Log. Quart. Vol. IX, 1962, pp. 181–186.

    Google Scholar 

  2. Dinkelbach, W.: Die Maximierung eines Quotienten zweier linearer Funktionen unter linearen Nebenbedingungen. — Z. Wahrscheinlichkeitstheorie, Vol. 1, 1962, pp. 141–145.

    Google Scholar 

  3. Dorn, W. S.: Linear fractional programming — I. B. M. Research Report, 1962.

  4. --: A duality theorem for convex programs. — I. B. M. Res. Jour. 4, 1960.

  5. Hadley, G.: Linear Programming. — Reading Mass: Addison Wesley, 1964.

    Google Scholar 

  6. Hanson, M. A.: Duality theorem in non-linear programming with non-linear constraints. — Australian Journal of Statistics, Vol. 3, 1961, pp. 64–71.

    Google Scholar 

  7. Kuhn, H. W. andA. W. Tucker: Non-Linear programming. — Proc. Second Berkeley Symposium on Math. Stat. and Prob. 1951, pp. 481–492.

  8. Martes, B.: Hyperbolic programming. — Nav. Res. Log. Quart., Vol. 11, 1964, pp. 135–155.

    Google Scholar 

  9. Swarup, K.: Linear fractional functionals programming. — Operations Res. vol. 13, No. 6, 1965, pp. 1029–1036.

    Google Scholar 

  10. --: Some aspects of linear fractional functionals programming. — Australian Journal of Statistics, Vol. 7, No. 3, 1965.

  11. ——: Transportation technique in linear fractional functionals programming. — J. R. N. S. S. Vol. 21, No. 5, 1966, pp. 256–260.

    Google Scholar 

  12. --: Fractional programming with non-linear constraints. — ZAMM, Vol. 46, No. 7, 1966.

  13. --: Some aspects of duality in fractional programming. — To appear in ZAMM, Vol. 47, 1967.

  14. ——: A duality theorem for non-linear programming. — ZAMM, Vol. 45, No. 5, 1965, pp. 311–314.

    Google Scholar 

  15. Wolfe, P.: Duality theorem for nonlinear programming. — Quart. Applied Maths., Oct. 1961, pp. 239–244.

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Authors and Affiliations

  1. Faculty of Mathematics, Delhi University, Delhi 7, India

    K. Swarup

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  1. K. Swarup
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Additional information

This work was done during my stay at the Indian Institute of Management, Calcutta, as a visiting faculty member.

Vorgel. v.:H. P. Künzi.

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Swarup, K. Duality in fractional programming. Unternehmensforschung Operations Research 12, 106–112 (1968). https://doi.org/10.1007/BF01918318

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  • DOI: https://doi.org/10.1007/BF01918318

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