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Duality for fractional interval-valued optimization problem via convexificator

Author

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  • B. Japamala Rani

    (School of Science, GITAM-Hyderabad Campus
    St. Ann’s College for Women-Mehdipatnam)

  • Krishna Kummari

    (School of Science, GITAM-Hyderabad Campus)

Abstract

In the current study, non-differentiable fractional interval-valued optimization problem (NFIVP) is studied by considering generalized invex functions. By using the optimality conditions, we investigate both types of dual problems namely Wolfe type and Mond-Weir type duals for (NFIVP) concerning invexity. Moreover, the suitable duality theorems are ascertained for both types of dual problems. Numerical examples are deliberated to substantiate the present work.

Suggested Citation

  • B. Japamala Rani & Krishna Kummari, 2023. "Duality for fractional interval-valued optimization problem via convexificator," OPSEARCH, Springer;Operational Research Society of India, vol. 60(1), pages 481-500, March.
    • Handle: RePEc:spr:opsear:v:60:y:2023:i:1:d:10.1007_s12597-022-00617-w
    DOI: 10.1007/s12597-022-00617-w
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    References listed on IDEAS

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    1. Bhatia, Davinder & Aggarwal, Shashi, 1992. "Optimality and duality for multiobjective nonsmooth programming," European Journal of Operational Research, Elsevier, vol. 57(3), pages 360-367, March.
    2. Do Luu & Tran Thi Mai, 2018. "Optimality and duality in constrained interval-valued optimization," 4OR, Springer, vol. 16(3), pages 311-337, September.
    3. H. C. Wu, 2010. "Duality Theory for Optimization Problems with Interval-Valued Objective Functions," Journal of Optimization Theory and Applications, Springer, vol. 144(3), pages 615-628, March.
    4. H. C. Wu, 2008. "Wolfe Duality for Interval-Valued Optimization," Journal of Optimization Theory and Applications, Springer, vol. 138(3), pages 497-509, September.
    5. Hsien-Chung Wu, 2011. "Duality Theory in Interval-Valued Linear Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 298-316, August.
    6. V. Jeyakumar & D. T. Luc, 1999. "Nonsmooth Calculus, Minimality, and Monotonicity of Convexificators," Journal of Optimization Theory and Applications, Springer, vol. 101(3), pages 599-621, June.
    7. Jianke Zhang, 2013. "Optimality Condition and Wolfe Duality for Invex Interval-Valued Nonlinear Programming Problems," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-11, December.
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    Cited by:

    1. Savin Treanţă & Omar Mutab Alsalami, 2024. "On a Weighting Technique for Multiple Cost Optimization Problems with Interval Values," Mathematics, MDPI, vol. 12(15), pages 1-10, July.

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