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Mond-Weir and Wolfe Duality of Set-Valued Fractional Minimax Problems in Terms of Contingent Epi-Derivative of Second-Order

Author

Listed:
  • Koushik Das

    (Department of Mathematics, Taki Government College, Taki 743429, India)

  • Savin Treanţă

    (Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania)

  • Tareq Saeed

    (Nonlinear Analysis and Applied Mathematics—Research Group, Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

Abstract

This paper is devoted to provide sufficient Karush Kuhn Tucker (in short, KKT) conditions of optimality of second-order for a set-valued fractional minimax problem. In addition, we define duals of the types Mond-Weir and Wolfe of second-order for the problem. Further we obtain the theorems of duality under contingent epi-derivative together with generalized cone convexity suppositions of second-order.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:938-:d:771428
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    References listed on IDEAS

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    1. S. J. Li & K. L. Teo & X. Q. Yang, 2008. "Higher-Order Optimality Conditions for Set-Valued Optimization," Journal of Optimization Theory and Applications, Springer, vol. 137(3), pages 533-553, June.
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    3. Johannes Jahn & Rüdiger Rauh, 1997. "Contingent epiderivatives and set-valued optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 46(2), pages 193-211, June.
    4. J. Jahn & A. A. Khan & P. Zeilinger, 2005. "Second-Order Optimality Conditions in Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 125(2), pages 331-347, May.
    5. 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.
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