Fractional Programming Problem with Bounded Parameters

  • A. K. Bhurjee
  • G. PandaEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 91)


In this paper, existence of the solution of a nonlinear fractional programming problem with parameters varying in some bounds, is studied. A general nonlinear programming problem, which is free from uncertain parameters, is formulated using the uncertain parameters of the original problem. Relation between the solution of the original problem and the transformed problem is established. The theoretical developments are justified in a numerical example.


Efficient solution Fractional programming problem Parametric optimization problem Interval valued function 


  1. 1.
    Bhurjee, A.K., G. Panda: Nonlinear fractional programming problem with inexact parameter. J. Appl. Math. Inform. 31, 853–867 (2013)Google Scholar
  2. 2.
    Bhurjee, A.K., Panda, G.: Efficient solution of interval optimization problem. Math. Methods Oper. Res. 76(3), 273–288 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Dinkelbach, Werner: On nonlinear fractional programming. Manag. Sci. 13(7), 492–498 (1967)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Hladik, M.: Generalized linear fractional programming under interval uncertainty. Eur. J. Oper. Res. 205, 42–46 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Hladik, Milan: Optimal value bounds in nonlinear programming with interval data. TOP 19(1), 93–106 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Hsien-Chung, Wu: On interval-valued nonlinear programming problems. J. Math. Anal. Appl. 338(1), 299–316 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Hsien-Chung, Wu: Duality theory in interval-valued linear programming problems. J. Optim. Theory Appl. 150, 298–316 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Ishibuchi, Hisao, Tanaka, Hideo: Multiobjective programming in optimization of the interval objective function. Eur. J. Oper. Res. 48(2), 219–225 (1990)CrossRefzbMATHGoogle Scholar
  9. 9.
    Jagannathan, R.: On some properties of programming problems in parametric form pertaining to fractional programming. INFORMS Manag. Sci. 12(7), 609–615 (1966)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Jayswal, A., Stancu-Minasian I., Ahmad, I.: On sufficiency and duality for a class of interval-valued programming problems. Appl. Math. Comput. 218(8), 4119–4127, (2011)Google Scholar
  11. 11.
    Jeyakumar, V., Li, G.Y.: Robust duality for fractional programming problems with constraint-wise data uncertainty. Eur. J. Oper. Res. 151(2), 292–303 (2011)Google Scholar
  12. 12.
    Levin, V.I.: Nonlinear optimization under interval uncertainty. Cybern. Syst. Anal. 35(2), 297–306 (1999)CrossRefzbMATHGoogle Scholar
  13. 13.
    Li, W., Tian, X.: Numerical solution method for general interval quadratic programming. Appl. Math. Comput. 202(2), 589–595 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Liu, Shiang-Tai, Wang, Rong-Tsu: A numerical solution method to interval quadratic programming. Appl. Math. Comput. 189(2), 1274–1281 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Liu, G., Jiang, C., Han, X., Liu, G.: A nonlinear interval number programming method for uncertain optimization problems. Eur. J. Oper. Res. 188(1), 1–13 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Moore, R.E.: Interval Analysis. Prentice-Hall, Englewood Cliffs (1966)Google Scholar
  17. 17.
    Schaible, Siegfried: Fractional programming. I Duality. Manag. Sci. 22(8), 858–867 (1976)CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Schaible, Siegfried, Ibaraki, Toshidide: Fractional programming. Eur. J. Oper. Res. 12(4), 325–338 (1983)CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    Shaocheng, T.: Interval number and fuzzy number linear programmings. Fuzzy Sets Syst. 66(3), 301–306 (1994)CrossRefGoogle Scholar
  20. 20.
    Wolf, Hartmut: A parametric method for solving the linear fractional programming problem. INFORMS Manag. Sci. 33(4), 835–841 (1985)zbMATHGoogle Scholar

Copyright information

© Springer India 2014

Authors and Affiliations

  1. 1.Indian Institute of Technology KharagpurKharagpurIndia

Personalised recommendations