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Duality in Fractional Programming: A Unified Approach

Author

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  • Siegfried Schaible

    (Stanford University, Stanford, California)

Abstract

This paper presents a unified method for obtaining duality results for concave-convex fractional programs. We obtain these results by transforming the original nonconvex programming problem into an equivalent convex program. Known results by several authors are related to each other. Moreover, we prove additional duality theorems, in particular, converse duality theorems for nondifferentiable as well as quadratic fractional programs.

Suggested Citation

  • Siegfried Schaible, 1976. "Duality in Fractional Programming: A Unified Approach," Operations Research, INFORMS, vol. 24(3), pages 452-461, June.
    • Handle: RePEc:inm:oropre:v:24:y:1976:i:3:p:452-461
    DOI: 10.1287/opre.24.3.452
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    Cited by:

    1. Frauke Liers & Lars Schewe & Johannes Thürauf, 2022. "Radius of Robust Feasibility for Mixed-Integer Problems," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 243-261, January.
    2. Paula Alexandra Amaral & Immanuel M. Bomze, 2019. "Nonconvex min–max fractional quadratic problems under quadratic constraints: copositive relaxations," Journal of Global Optimization, Springer, vol. 75(2), pages 227-245, October.
    3. 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.
    4. 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.
    5. T Peña & P Lara & C Castrodeza, 2009. "Multiobjective stochastic programming for feed formulation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(12), pages 1738-1748, December.
    6. Maziar Sahamkhadam & Andreas Stephan, 2023. "Portfolio optimization based on forecasting models using vine copulas: An empirical assessment for global financial crises," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(8), pages 2139-2166, December.
    7. Xiaojun Lei & Zhian Liang, 2008. "Study on the Duality between MFP and ACP," Modern Applied Science, Canadian Center of Science and Education, vol. 2(6), pages 1-81, November.
    8. C. Singh & M.A. Hanson, 1991. "Multiobjective fractional programming duality theory," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(6), pages 925-933, December.
    9. Altannar Chinchuluun & Dehui Yuan & Panos Pardalos, 2007. "Optimality conditions and duality for nondifferentiable multiobjective fractional programming with generalized convexity," Annals of Operations Research, Springer, vol. 154(1), pages 133-147, October.

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