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Duality and Sensitivity Analysis for Fractional Programs

Author

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  • Gabriel R. Bitran

    (University of Sao Paulo, Sao Paulo, Brazil)

  • Thomas L. Magnanti

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

In this paper we consider algorithms, duality and sensitivity analysis for optimization problems, called fractional, whose objective function is the ratio of two real-valued functions. We discuss a procedure suggested by Dinkelbach for solving the problem, its relation to certain approaches via variable transformations, and a variant of the procedure that has convenient convergence properties. The duality correspondences that are developed do not require either differentiability or the existence of an optimal solution. The sensitivity analysis applies to linear fractional problems, even when they “solve” at an extreme ray, and includes a primal-dual algorithm for parametric right-hand-side analysis.

Suggested Citation

  • Gabriel R. Bitran & Thomas L. Magnanti, 1976. "Duality and Sensitivity Analysis for Fractional Programs," Operations Research, INFORMS, vol. 24(4), pages 675-699, August.
    • Handle: RePEc:inm:oropre:v:24:y:1976:i:4:p:675-699
    DOI: 10.1287/opre.24.4.675
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    Cited by:

    1. Oleksii Ursulenko & Sergiy Butenko & Oleg Prokopyev, 2013. "A global optimization algorithm for solving the minimum multiple ratio spanning tree problem," Journal of Global Optimization, Springer, vol. 56(3), pages 1029-1043, July.
    2. Bajalinov, Erik B., 1999. "On an approach to the modelling of problems connected with conflicting economic interests," European Journal of Operational Research, Elsevier, vol. 116(3), pages 477-486, August.
    3. Danny Z. Chen & Ovidiu Daescu & Yang Dai & Naoki Katoh & Xiaodong Wu & Jinhui Xu, 2005. "Efficient Algorithms and Implementations for Optimizing the Sum of Linear Fractional Functions, with Applications," Journal of Combinatorial Optimization, Springer, vol. 9(1), pages 69-90, February.
    4. Juan S. Borrero & Colin Gillen & Oleg A. Prokopyev, 2017. "Fractional 0–1 programming: applications and algorithms," Journal of Global Optimization, Springer, vol. 69(1), pages 255-282, September.

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