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

#### **Ramu Dubey 1, Vishnu Narayan Mishra 2,\*, and Rifaqat Ali 3**


Received: 5 September 2019; Accepted: 15 October 2019; Published: 3 November 2019

**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 (*<sup>V</sup>*, *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.

**Keywords:** duality; support function; nondifferentiable; strictly pseudo (*<sup>V</sup>*, *α*, *ρ*, *d*)-type-I; unified dual; efficient solutions
