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Duality for Unified Higher-Order Minimax Fractional Programming with Support Function under Type-I Assumptions

Author

Listed:
  • Ramu Dubey

    (Department of Mathematics, J C Bose University of Science and Technology, YMCA, Faridabad 121006, India)

  • Vishnu Narayan Mishra

    (Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, Madhya Pradesh 484887, India)

  • Rifaqat Ali

    (Department of Mathematics, College of Science and Arts, Muhayil, King Khalid University, 61413 Abha, Saudi Arabia)

Abstract

This article is devoted to discussing the nondifferentiable minimax fractional programming problem with type-I functions. We focus our study on a nondifferentiable minimax fractional programming problem and formulate a higher-order dual model. Next, we establish weak, strong, and strict converse duality theorems under generalized higher-order strictly pseudo ( V , α , ρ , d ) -type-I functions. In the final section, we turn our focus to study a nondifferentiable unified minimax fractional programming problem and the results obtained in this paper naturally unify. Further, we extend some previously known results on nondifferentiable minimax fractional programming in the literature.

Suggested Citation

  • Ramu Dubey & Vishnu Narayan Mishra & Rifaqat Ali, 2019. "Duality for Unified Higher-Order Minimax Fractional Programming with Support Function under Type-I Assumptions," Mathematics, MDPI, vol. 7(11), pages 1-12, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1034-:d:283090
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    References listed on IDEAS

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    1. D. H. Yuan & X. L. Liu & A. Chinchuluun & P. M. Pardalos, 2006. "Nondifferentiable Minimax Fractional Programming Problems with (C, α, ρ, d)-Convexity," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 185-199, April.
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