Zeitschrift für Operations Research

, Volume 18, Issue 5, pp 187–196 | Cite as

Parameter-free convex equivalent and dual programs of fractional programming problems

  • S. Schaible


An appropriate generalization ofCharnes-Cooper's [1962] variable transformation is introduced, by which a parameter-free convex program is associated to nonlinear fractional programs. The equivalent program also enables a direct approach toJagannathan's. [1973] duality theory simultaneously extending it. In particular for some special cases further duality theorems are derived.


Programming Problem Direct Approach Duality Theory Convex Program Duality Theorem 
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Durch geeignete Verallgemeinerung der Variablentransformation vonCharnes-Cooper [1962] wird nichtlinearen Quotientenprogrammen ein parameterfreies konvexes Programm zugeordnet. Dieses ermöglicht auch einen direkten Zugang zuJagannathans [1973] Dualitätstheorie, die gleichzeitig erweitert wird. Insbesondere werden für einige Spezialfälle weitere Dualitätssätze abgeleitet.


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  1. Bector, C. R.: Duality in nonlinear fractional programming, Zeitschrift f. Oper. Res.17, 183–193, 1973.Google Scholar
  2. Charnes, A., andW. W. Cooper: Programming with Linear Fractional Functional, Naval Research Logistics Quarterly9, 181–196, 1962.Google Scholar
  3. Dinkelbach, W.: On Nonlinear Fractional Programming, Management Science13, 492–498, 1967.Google Scholar
  4. Dorn, W. S.: Duality in Quadratic Programming, Quarterly of Applied Mathematics18, 155–162, 1960.Google Scholar
  5. Geoffrion, A. M.: Strictly Concave Parametric Programming, Part I: Basic Theory, Management Science13. 244–253. 1967. Part II: Additional Theory and Computational Considerations. Management Science13, 359–370, 1967a.Google Scholar
  6. —: Solving Bi-criterion Mathematical Programs, Oper. Res.15, 39–54, 1967b.Google Scholar
  7. Jagannathan, R.: On Some Properties of Programming Problems in Parametric Form Pertaining to Fractional Programming, Management Science12, 609–615, 1966.Google Scholar
  8. —: Duality for Nonlinear Fractional Programs, Zeitschrift für Operations Research17, 1–3, 1973.Google Scholar
  9. Manas, M.: On Transformations of Quasi-convex Programming Problems, Ekon. Matem. Obzor, Ceskoslovenska Akademie VED, 93–99, 1968.Google Scholar
  10. Mangasarian, O. L.: Pseudo-convex Functions, J. SIAM Control, Ser. A3, 281–290, 1965.Google Scholar
  11. -: Nonlinear Programming, New York 1969.Google Scholar
  12. van de Panne, C.: Programming with a Quadratic Constraint, Management Science12, 798–815, 1966.Google Scholar
  13. Schaible, S.: Transformationen nichtlinearer Quotientenprogramme in konvexe Programme, presented at the Annual Meeting of the German Society of Operations Research 1972, appears in “Proceedings of Operations Research≓, 351–361, 1973.Google Scholar
  14. -: Maximization of Quasi-concave Quotients and Products of Finitely Many Functionals, to be published in Cahiers du Centre d'Etudes de Recherche Operationelle 1974.Google Scholar
  15. Sharma, I. C., andK. Swarup: On Duality in Linear Fractional Functionals Programming, Zeitschrift für Operations Research17, 91–100, 1972.Google Scholar
  16. Wolfe, P.: A Duality Theorem for Nonlinear Programming, Quarterly of Applied Mathematics19, 239–244. 1961.Google Scholar

Copyright information

© Physica-Verlag 1974

Authors and Affiliations

  • S. Schaible
    • 1
  1. 1.Seminar für Allgemeine und Industrielle BetriebswirtschaftslehreUniversität KölnKöln

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