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Generalized fractional programming: Optimality and duality theory

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Abstract

The generalized fractional programming problem with a finite number of ratios in the objective is studied. Optimality and duality results are established, some with the help of an auxiliary problem and some directly. Convexity and stability of the auxiliary problem play a key role in the latter part of the paper.

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References

  1. Isbell, J. R., andMarlow, W. H.,Attribution Games, Naval Research Logistics Quarterly, Vol. 3, pp. 71–93, 1956.

    Google Scholar 

  2. Schaible, S.,A Survey of Fractional Programming, Generalized Concavity in Optimization and Economics, Edited by S. Schaible and W. T. Ziemba, Academic Press, New York, New York, pp. 417–440, 1981.

    Google Scholar 

  3. Singh, C., andHanson, M. A.,Saddlepoint Theory for Nondifferentiable Multiobjective Fractional Programming, Journal of Information and Optimization Sciences, Vol. 7, pp. 41–48, 1986.

    Google Scholar 

  4. Singh, C.,A Class of Multiple Criteria Fractional Programming Problems, Journal of Mathematical Analysis and Applications, Vol. 115, pp. 202–213, 1986.

    Google Scholar 

  5. Singh, C., andHanson, M. A.,Multiobjective Fractional Programming Duality Theory (submitted).

  6. Crouzeix, J. P.,A Duality Framework in Quasi-Convex Programming, Generalized Concavity in Optimization and Economics, Edited by S. Schaible and W. T. Ziemba, Academic Press, New York, New York, pp. 207–225, 1981.

    Google Scholar 

  7. Crouzeix, J. P., Ferland, J. A., andSchaible, S.,Duality in Generalized Fractional Programming, Mathematical Programming, Vol. 27, pp. 342–354, 1983.

    Google Scholar 

  8. Jagannathan, R., andSchaible, S.,Duality in Generalized Fractional Programming via Farkas' Lemma, Journal of Optimization Theory and Applications, Vol. 41, pp. 417–424, 1983.

    Google Scholar 

  9. Chandra, S., Craven, B. D., andMond, B.,Generalized Fractional Programming Duality: A Ratio Game Approach, Department of Mathematics, University of Melbourne, Melbourne, Australia, Research Report No. 23, 1983.

    Google Scholar 

  10. Bector, K., Hussain, I., Chandra, S., andBector, C. R.,A Duality Model for a Generalized Minmax Program, Naval Research Logistics, Vol. 35, pp. 493–501, 1988.

    Google Scholar 

  11. Bector, C. R., Chandra, S., andBector, M. K.,Generalized Fractional Programming Duality: A Parametric Approach, Journal of Optimization Theory and Applications, Vol. 60, pp. 243–260, 1989.

    Google Scholar 

  12. Mond, B., andWeir, T.,Generalized Concavity and Duality, Generalized Concavity in Optimization and Economics, Edited by S. Schaible and W. T. Ziemba, Academic Press, New York, New York, pp. 263–279, 1981.

    Google Scholar 

  13. Singh, C.,Optimality Conditions for Fractional Minmax Programming, Journal of Mathematical Analysis and Applications, Vol. 100, pp. 409–415, 1984.

    Google Scholar 

  14. Xu, Z. K.,Saddle-Point Type Optimality Criteria for Generalized Fractional Programming, Journal of Optimization Theory and Applications, Vol. 57, pp. 189–196, 1988.

    Google Scholar 

  15. Geoffrion, A. M.,Duality in Nonlinear Programming: A Simplified Applications-Oriented Development, SIAM Review, Vol. 13, pp. 1–37, 1971.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, St. Lawrence University, Canton, New York

    C. Singh (Professor) & N. Rueda (Assistant Professor)

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  1. C. Singh
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  2. N. Rueda
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Additional information

Communicated by R. A. Tapia

The authors are grateful to an unknown referee for suggesting the statement of Theorem 3.3.

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Singh, C., Rueda, N. Generalized fractional programming: Optimality and duality theory. J Optim Theory Appl 66, 149–159 (1990). https://doi.org/10.1007/BF00940538

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