Conjugate duality in generalized fractional programming

  • C. H. Scott
  • T. R. Jefferson
Contributed Papers


The concepts of conjugate duality are used to establish dual programs for a class of generalized nonlinear fractional programs. It is now known that, under certain restrictions, a symmetric duality exists for generalized linear fractional programs. In this paper, we establish this symmetric duality for the nonlinear case.

Key Words

Conjugate functions convex analysis duality generalized fractional programs 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Schaible, S.,Fractional Programming, Zeitschrift für Operations Research, Vol. 27, pp. 39–54, 1983.Google Scholar
  2. 2.
    Crouzeix, J., Ferland, J., andSchaible, S.,Duality in Generalized LInear Fractional Programming, Mathematical Programming, Vol. 27, pp. 342–354, 1983.Google Scholar
  3. 3.
    Crouzeix, J. P.,Contributions à l'Etude des Functions Quasiconvexes, Université de Clermont, Doctoral Dissertation, 1977.Google Scholar
  4. 4.
    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
  5. 5.
    Crouzeix, J. P.,A Duality Framework in Quasiconvex Programming, Generalized Concavity in Optimization and Economics, Edited by S. Schaible and W. T. Ziemba, Academic Press, New York, New York, pp. 207–236, 1981.Google Scholar
  6. 6.
    Chandra, S., Craven, B., andMond, B.,Generalized Fractional Programming Duality: A Ratio Game Approach, Journal of Australian Mathematical Society, Series B, Vol. 28, pp. 170–180, 1986.Google Scholar
  7. 7.
    Fenchel, W.,Convex Cones, Sets, and Functions, Princeton University Press, Princeton, New Jersey, 1953.Google Scholar
  8. 8.
    Rockafellar, R. T.,Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.Google Scholar
  9. 9.
    Peterson, E. L.,Geometric Programming, SIAM Review, Vol. 18, pp. 1–52, 1976.Google Scholar
  10. 10.
    Scott, C. H., andJefferson, T. R.,Fractional Programming Duality via Geometric Programming Duality, Journal of the Australian Mathematical Society, Series B, Vol. 21, pp. 398–401, 1980.Google Scholar

Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • C. H. Scott
    • 1
  • T. R. Jefferson
    • 2
  1. 1.Graduate School of ManagementUniversity of CaliforniaIrvine
  2. 2.A. B. Freeman School of BusinessTulane UniversityNew Orleans

Personalised recommendations