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Robust Duality for Fractional Programming Problems with Constraint-Wise Data Uncertainty

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  • V. Jeyakumar

    (University of New South Wales)

  • G. Y. Li

    (University of New South Wales)

Abstract

In this paper, we examine duality for fractional programming problems in the face of data uncertainty within the framework of robust optimization. We establish strong duality between the robust counterpart of an uncertain convex–concave fractional program and the optimistic counterpart of its conventional Wolfe dual program with uncertain parameters. For linear fractional programming problems with constraint-wise interval uncertainty, we show that the dual of the robust counterpart is the optimistic counterpart in the sense that they are equivalent. Our results show that a worst-case solution of an uncertain fractional program (i.e., a solution of its robust counterpart) can be obtained by solving a single deterministic dual program. In the case of a linear fractional programming problem with interval uncertainty, such solutions can be found by solving a simple linear program.

Suggested Citation

  • V. Jeyakumar & G. Y. Li, 2011. "Robust Duality for Fractional Programming Problems with Constraint-Wise Data Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 292-303, November.
    • Handle: RePEc:spr:joptap:v:151:y:2011:i:2:d:10.1007_s10957-011-9896-1
    DOI: 10.1007/s10957-011-9896-1
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    References listed on IDEAS

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    1. Z. A. Liang & H. X. Huang & P. M. Pardalos, 2001. "Optimality Conditions and Duality for a Class of Nonlinear Fractional Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 110(3), pages 611-619, September.
    2. Jeyakumar, V. & Li, G., 2010. "New strong duality results for convex programs with separable constraints," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1203-1209, December.
    3. 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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    Cited by:

    1. A. Bhurjee & G. Panda, 2012. "Efficient solution of interval optimization problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(3), pages 273-288, December.
    2. Jeyakumar, V. & Li, G.Y. & Srisatkunarajah, S., 2013. "Strong duality for robust minimax fractional programming problems," European Journal of Operational Research, Elsevier, vol. 228(2), pages 331-336.
    3. Jiawei Chen & Suliman Al-Homidan & Qamrul Hasan Ansari & Jun Li & Yibing Lv, 2021. "Robust Necessary Optimality Conditions for Nondifferentiable Complex Fractional Programming with Uncertain Data," Journal of Optimization Theory and Applications, Springer, vol. 189(1), pages 221-243, April.
    4. Morteza Rahimi & Majid Soleimani-damaneh, 2020. "Characterization of Norm-Based Robust Solutions in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 554-573, May.
    5. Yanjun Wang & Ruizhi Shi & Jianming Shi, 2015. "Duality and robust duality for special nonconvex homogeneous quadratic programming under certainty and uncertainty environment," Journal of Global Optimization, Springer, vol. 62(4), pages 643-659, August.
    6. P. Kumar & G. Panda, 2017. "Solving nonlinear interval optimization problem using stochastic programming technique," OPSEARCH, Springer;Operational Research Society of India, vol. 54(4), pages 752-765, December.
    7. Nguyen Dinh & Miguel Angel Goberna & Marco Antonio López & Michel Volle, 2017. "A Unifying Approach to Robust Convex Infinite Optimization Duality," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 650-685, September.
    8. Debdas Ghosh, 2016. "A Newton method for capturing efficient solutions of interval optimization problems," OPSEARCH, Springer;Operational Research Society of India, vol. 53(3), pages 648-665, September.

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