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Robust Necessary Optimality Conditions for Nondifferentiable Complex Fractional Programming with Uncertain Data

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  • Jiawei Chen

    (Southwest University)

  • Suliman Al-Homidan

    (King Fahd University of Petroleum and Minerals)

  • Qamrul Hasan Ansari

    (King Fahd University of Petroleum and Minerals
    Aligarh Muslim University)

  • Jun Li

    (Southwest University)

  • Yibing Lv

    (Yangtze University)

Abstract

In this paper, we study robust necessary optimality conditions for a nondifferentiable complex fractional programming with uncertain data. A robust counterpart of uncertain complex fractional programming is introduced in the worst-case scenario. The concept of robust optimal solution of the uncertain complex fractional programming is introduced by using robust counterpart. We give an equivalence between the optimal solutions of the robust counterpart and a minimax nonfractional parametric programming. Finally, Fritz John-type and Karush–Kuhn–Tucker-type robust necessary optimality conditions of the uncertain complex fractional programming are established under some suitable conditions.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:189:y:2021:i:1:d:10.1007_s10957-021-01829-8
    DOI: 10.1007/s10957-021-01829-8
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    References listed on IDEAS

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    1. Jiawei Chen & Jun Li & Xiaobing Li & Yibing Lv & Jen-Chih Yao, 2020. "Radius of Robust Feasibility of System of Convex Inequalities with Uncertain Data," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 384-399, February.
    2. J. C. Chen & H. C. Lai & S. Schaible, 2005. "Complex Fractional Programming and the Charnes-Cooper Transformation," Journal of Optimization Theory and Applications, Springer, vol. 126(1), pages 203-213, July.
    3. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    4. Jiawei Chen & Elisabeth Köbis & Jen-Chih Yao, 2019. "Optimality Conditions and Duality for Robust Nonsmooth Multiobjective Optimization Problems with Constraints," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 411-436, May.
    5. A. L. Soyster, 1973. "Technical Note—Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming," Operations Research, INFORMS, vol. 21(5), pages 1154-1157, October.
    6. H. C. Lai & J. C. Liu & S. Schaible, 2008. "Complex Minimax Fractional Programming of Analytic Functions," Journal of Optimization Theory and Applications, Springer, vol. 137(1), pages 171-184, April.
    7. Xiangkai Sun & Kok Lay Teo & Liping Tang, 2019. "Dual Approaches to Characterize Robust Optimal Solution Sets for a Class of Uncertain Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 984-1000, September.
    8. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    9. Chenchen Wu & Dachuan Xu & Donglei Du & Wenqing Xu, 2016. "An approximation algorithm for the balanced Max-3-Uncut problem using complex semidefinite programming rounding," Journal of Combinatorial Optimization, Springer, vol. 32(4), pages 1017-1035, November.
    10. 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.
    11. Bram L. Gorissen, 2015. "Robust Fractional Programming," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 508-528, August.
    12. Werner Dinkelbach, 1967. "On Nonlinear Fractional Programming," Management Science, INFORMS, vol. 13(7), pages 492-498, March.
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    Cited by:

    1. Jie Wang & Shengjie Li & Min Feng, 2022. "Unified Robust Necessary Optimality Conditions for Nonconvex Nonsmooth Uncertain Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 226-248, October.

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