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Open AccessArticle

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

1
Department of Mathematics, J C Bose University of Science and Technology, YMCA, Faridabad 121006, India
2
Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, Madhya Pradesh 484887, India
3
Department of Mathematics, College of Science and Arts, Muhayil, King Khalid University, 61413 Abha, Saudi Arabia
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(11), 1034; https://doi.org/10.3390/math7111034
Received: 5 September 2019 / Revised: 10 October 2019 / Accepted: 15 October 2019 / Published: 3 November 2019
(This article belongs to the Special Issue Multivariate Approximation for solving ODE and PDE)
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. View Full-Text
Keywords: duality; support function; nondifferentiable; strictly pseudo (V,α,ρ,d)-type-I; unified dual; efficient solutions duality; support function; nondifferentiable; strictly pseudo (V,α,ρ,d)-type-I; unified dual; efficient solutions
MDPI and ACS Style

Dubey, R.; Mishra, V.N.; Ali, R. Duality for Unified Higher-Order Minimax Fractional Programming with Support Function under Type-I Assumptions. Mathematics 2019, 7, 1034.

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