On nondifferentiable minimax fractional programming under generalized α-type I invexity

Abstract

In this paper, we study a nondifferentiable minimax fractional programming problem under the assumptions of generalized α-type I invex function. In this paper we introduce the concepts of α-type I invex, pseudo α-type I invex, strict pseudo α-type I invex and quasi α-type I invex functions in the setting of Clarke subdifferential functions. We derive Karush-Kuhn-Tucker type sufficient optimality conditions and establish weak, strong and converse duality theorems for the problem and its three different dual problems. The results in this paper extend several known results in the literature.