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Fractional Programming

Author

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  • Frenk, J.B.G.
  • Schaible, S.

Abstract

Single-ratio and multi-ratio fractional programs in applications are often generalized convex programs. We begin with a survey of applications of single-ratio fractional programs, min-max fractional programs and sum-of-ratios fractional programs. Given the limited advances for the latter class of problems, we focus on an analysis of min-max fractional programs. A parametric approach is employed to develop both theoretical and algorithmic results.

Suggested Citation

  • Frenk, J.B.G. & Schaible, S., 2004. "Fractional Programming," ERIM Report Series Research in Management ERS-2004-074-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    • Handle: RePEc:ems:eureri:1610
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    References listed on IDEAS

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    1. Siegfried Schaible, 1976. "Fractional Programming. I, Duality," Management Science, INFORMS, vol. 22(8), pages 858-867, April.
    2. Birbil, S.I. & Frenk, J.B.G. & Zhang, S., 2004. "Generalized Fractional Programming With User Interaction," Econometric Institute Research Papers ERS-2004-033-LIS, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. Bazsa-Oldenkamp, E.M. & Frenk, J.B.G. & den Iseger, P., 1998. "Inventory control and regenerative processes," Econometric Institute Research Papers EI 9848, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    4. Goedhart, Marc H. & Spronk, Jaap, 1995. "Financial planning with fractional goals," European Journal of Operational Research, Elsevier, vol. 82(1), pages 111-124, April.
    5. Frenk, J. B. G. & Kassay, G. & Kolumban, J., 2004. "On equivalent results in minimax theory," European Journal of Operational Research, Elsevier, vol. 157(1), pages 46-58, August.
    6. Martin Gugat, 1996. "A Fast Algorithm for a Class of Generalized Fractional Programs," Management Science, INFORMS, vol. 42(10), pages 1493-1499, October.
    7. Birbil, S.I. & Frenk, J.B.G. & Zhang, S., 2004. "Generalized Fractional Programming With User Interaction," ERIM Report Series Research in Management ERS-2004-033-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    8. Sniedovich, Moshe, 1988. "Fractional programming revisited," European Journal of Operational Research, Elsevier, vol. 33(3), pages 334-341, February.
    9. Bazsa, E. M. & Frenk, J. B. G. & den Iseger, P. W., 2001. "Modeling of inventory control with regenerative processes," International Journal of Production Economics, Elsevier, vol. 71(1-3), pages 263-276, May.
    10. Schaible, Siegfried, 1981. "Fractional programming: Applications and algorithms," European Journal of Operational Research, Elsevier, vol. 7(2), pages 111-120, June.
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    Citations

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    Cited by:

    1. Smail Addoune & Karima Boufi & Ahmed Roubi, 2018. "Proximal Bundle Algorithms for Nonlinearly Constrained Convex Minimax Fractional Programs," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 212-239, October.
    2. H. Boualam & A. Roubi, 2019. "Proximal bundle methods based on approximate subgradients for solving Lagrangian duals of minimax fractional programs," Journal of Global Optimization, Springer, vol. 74(2), pages 255-284, June.
    3. Yong Xia & Longfei Wang & Xiaohui Wang, 2020. "Globally minimizing the sum of a convex–concave fraction and a convex function based on wave-curve bounds," Journal of Global Optimization, Springer, vol. 77(2), pages 301-318, June.
    4. Benson, Harold P., 2006. "Fractional programming with convex quadratic forms and functions," European Journal of Operational Research, Elsevier, vol. 173(2), pages 351-369, September.
    5. João Costa & Maria Alves, 2013. "Enhancing computations of nondominated solutions in MOLFP via reference points," Journal of Global Optimization, Springer, vol. 57(3), pages 617-631, November.
    6. Yong Xia & Longfei Wang & Meijia Yang, 2019. "A fast algorithm for globally solving Tikhonov regularized total least squares problem," Journal of Global Optimization, Springer, vol. 73(2), pages 311-330, February.

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    More about this item

    Keywords

    Single-ratio fractional programs; applications of fractional programs to management science and engineering; generalized fractional programs; min-max fractional programs; parametric approach; sum-of-ratios fractional programs;
    All these keywords.

    JEL classification:

    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other
    • M - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics
    • M11 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - Production Management
    • R4 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics

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