On nondifferentiable minimax fractional programming involving higher order generalized convexity

Abstract

In this article, we focus our study on a nondifferentiable minimax fractional programming problem and establish weak, strong and strict converse duality theorems under generalized higher order (F , α, ρ, d)-Type I assumptions. Our results extend and unify some of the known results in the literature.

Minimax fractional programming with nondiferentiable (G,β)-invexity

“…In particular, they have also been applied to deal with minimax programming; see [13][14][15][16][17] for detail. Moreover, some researchers, for example [20] and [21], considered the minimax fractional programming involving higher order generalized convexity. However, we have not found paper which deal with minimax fractional programming Problem (FP) under assumptions of G-invexity or its generalizations.…”

Nondifferentiable Minimax Programming Problems in Complex Spaces Involving Generalized Convex Functions

“…Later on, Jayswal et al [7] extended the work of Ahmad and Husain [6] to establish sufficient optimality conditions and duality theorems for the nondifferentiable minimax fractional problem under the assumptions of generalized ( , , , )-convexity. Recently, Jayswal and Kumar [8] established sufficient optimality conditions and duality theorems for a class of nondifferentiable minimax fractional programming problems under the assumptions of ( , , , )-convexity. Lai et al [9] established several sufficient optimality conditions for minimax programming in complex spaces under the assumptions of generalized convexity of complex functions.…”