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Optimality Conditions and Duality in Nondifferentiable Minimax Fractional Programming with Generalized Convexity

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  • I. Ahmad

    (Aligarh Muslim University)

  • Z. Husain

    (Aligarh Muslim University)

Abstract

We establish sufficient optimality conditions for a class of nondifferentiable minimax fractional programming problems involving (F, α, ρ, d)-convexity. Subsequently, we apply the optimality conditions to formulate two types of dual problems and prove appropriate duality theorems.

Suggested Citation

  • I. Ahmad & Z. Husain, 2006. "Optimality Conditions and Duality in Nondifferentiable Minimax Fractional Programming with Generalized Convexity," Journal of Optimization Theory and Applications, Springer, vol. 129(2), pages 255-275, May.
    • Handle: RePEc:spr:joptap:v:129:y:2006:i:2:d:10.1007_s10957-006-9057-0
    DOI: 10.1007/s10957-006-9057-0
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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.
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    Cited by:

    1. I. Ahmad & Z. Husain & S. Sharma, 2009. "Higher-Order Duality in Nondifferentiable Minimax Programming with Generalized Type I Functions," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 1-12, April.
    2. Koushik Das & Savin Treanţă & Tareq Saeed, 2022. "Mond-Weir and Wolfe Duality of Set-Valued Fractional Minimax Problems in Terms of Contingent Epi-Derivative of Second-Order," Mathematics, MDPI, vol. 10(6), pages 1-21, March.
    3. Sonali & N. Kailey & V. Sharma, 2016. "On second order duality of minimax fractional programming with square root term involving generalized B-(p, r)-invex functions," Annals of Operations Research, Springer, vol. 244(2), pages 603-617, September.
    4. Anurag Jayswal & Ashish Kumar Prasad & Krishna Kummari, 2013. "Nondifferentiable Minimax Programming Problems in Complex Spaces Involving Generalized Convex Functions," Journal of Optimization, Hindawi, vol. 2013, pages 1-12, December.
    5. Hang-Chin Lai & Hui-Mei Chen, 2012. "Duality on a nondifferentiable minimax fractional programming," Journal of Global Optimization, Springer, vol. 54(2), pages 295-306, October.

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