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

• Main Authors: Ramu Dubey, Vishnu Narayan Mishra, Rifaqat Ali
• Format: Article
• Language: English
• Published: MDPI AG 2019-11-01
• Series: Mathematics
• Subjects: duality; support function; nondifferentiable; strictly pseudo (v,α,ρ,d)-type-i; unified dual; efficient solutions
• Online Access: https://www.mdpi.com/2227-7390/7/11/1034

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 <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>V</mi> <mo>,</mo> <mi>&#945;</mi> <mo>,</mo> <mi>&#961;</mi> <mo>,</mo> <mi>d</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-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.