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Generic Algorithm for Generalized Fractional Programming

Author

Listed:
  • H. J. Chen

    (National Cheng Kung University)

  • S. Schaible

    (University of California
    Chung Yuan Christian University)

  • R. L. Sheu

    (National Cheng Kung University)

Abstract

We propose a unified framework to study various versions of Dinkelbach-type algorithms for solving the generalized fractional programming problem. Classical algorithms used carefully selected iterate points and incorporated subtle convergence proofs. Our generic algorithm, however, is natural and simple. Moreover, the convergence analysis can be carried out through geometric observations and fundamental properties of convex functions. Consequently, the classical results are either refined or strengthened with new insights.

Suggested Citation

  • H. J. Chen & S. Schaible & R. L. Sheu, 2009. "Generic Algorithm for Generalized Fractional Programming," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 93-105, April.
    • Handle: RePEc:spr:joptap:v:141:y:2009:i:1:d:10.1007_s10957-008-9499-7
    DOI: 10.1007/s10957-008-9499-7
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    References listed on IDEAS

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    1. J. Y. Lin & R. L. Sheu, 2005. "Modified Dinkelbach-Type Algorithm for Generalized Fractional Programs with Infinitely Many Ratios," Journal of Optimization Theory and Applications, Springer, vol. 126(2), pages 323-343, August.
    2. R. L. Sheu & J. Y. Lin, 2004. "Solving Continuous Min-Max Problems by an Iterative Entropic Regularization Method," Journal of Optimization Theory and Applications, Springer, vol. 121(3), pages 597-612, June.
    3. Y. Almogy & O. Levin, 1971. "A Class of Fractional Programming Problems," Operations Research, INFORMS, vol. 19(1), pages 57-67, February.
    4. Ferland, Jacques A. & Potvin, Jean-Yves, 1985. "Generalized fractional programming: Algorithms and numerical experimentation," European Journal of Operational Research, Elsevier, vol. 20(1), pages 92-101, April.
    5. J. v. Neumann, 1945. "A Model of General Economic Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 13(1), pages 1-9.
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    Cited by:

    1. Jae Hyoung Lee & Liguo Jiao, 2018. "Solving Fractional Multicriteria Optimization Problems with Sum of Squares Convex Polynomial Data," Journal of Optimization Theory and Applications, Springer, vol. 176(2), pages 428-455, February.
    2. Jiao, Hongwei & Li, Binbin, 2022. "Solving min–max linear fractional programs based on image space branch-and-bound scheme," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Michele Garraffa & Federico Della Croce & Fabio Salassa, 2017. "An exact semidefinite programming approach for the max-mean dispersion problem," Journal of Combinatorial Optimization, Springer, vol. 34(1), pages 71-93, July.
    4. Bram L. Gorissen, 2015. "Robust Fractional Programming," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 508-528, August.

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