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Fractional Programming with Homogeneous Functions

Author

Listed:
  • Stephen P. Bradley

    (Graduate School of Business Administration, Harvard University, Boston, Massachusetts)

  • Sherwood C. Frey

    (Graduate School of Business Administration, Harvard University, Boston, Massachusetts)

Abstract

This paper extends the well known results for linear fractional programming to the class of programming problems involving the ratio of nonlinear functionals subject to nonlinear constraints, where the constraints are homogeneous of degree one and the functionals are homogeneous of degree one to within a constant. Two rather general auxiliary problems are developed, and the relations between the solutions of the auxiliary problems and the solutions of the original problem are codified. Applications of the results for specific problems are also presented.

Suggested Citation

  • Stephen P. Bradley & Sherwood C. Frey, 1974. "Fractional Programming with Homogeneous Functions," Operations Research, INFORMS, vol. 22(2), pages 350-357, April.
    • Handle: RePEc:inm:oropre:v:22:y:1974:i:2:p:350-357
    DOI: 10.1287/opre.22.2.350
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    Cited by:

    1. Yaohua Hu & Carisa Kwok Wai Yu & Xiaoqi Yang, 2019. "Incremental quasi-subgradient methods for minimizing the sum of quasi-convex functions," Journal of Global Optimization, Springer, vol. 75(4), pages 1003-1028, December.
    2. Xiaoqi Yang & Chenchen Zu, 2022. "Convergence of Inexact Quasisubgradient Methods with Extrapolation," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 676-703, June.
    3. W. Cooper & Z. Huang & S. Li & J. Zhu, 2008. "A response to the critiques of DEA by Dmitruk and Koshevoy, and Bol," Journal of Productivity Analysis, Springer, vol. 29(1), pages 15-21, February.
    4. Hishinuma, Kazuhiro & Iiduka, Hideaki, 2020. "Fixed point quasiconvex subgradient method," European Journal of Operational Research, Elsevier, vol. 282(2), pages 428-437.
    5. Hu, Yaohua & Li, Gongnong & Yu, Carisa Kwok Wai & Yip, Tsz Leung, 2022. "Quasi-convex feasibility problems: Subgradient methods and convergence rates," European Journal of Operational Research, Elsevier, vol. 298(1), pages 45-58.
    6. Dey, Shibshankar & Kim, Cheolmin & Mehrotra, Sanjay, 2024. "An algorithm for stochastic convex-concave fractional programs with applications to production efficiency and equitable resource allocation," European Journal of Operational Research, Elsevier, vol. 315(3), pages 980-990.
    7. Hu, Yaohua & Yang, Xiaoqi & Sim, Chee-Khian, 2015. "Inexact subgradient methods for quasi-convex optimization problems," European Journal of Operational Research, Elsevier, vol. 240(2), pages 315-327.

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