Non-differentiable minimax fractional programming with generalized [formula omitted]-univexity

Abstract

In this paper, we study a non-differentiable minimax fractional programming problem under the assumption of generalized α -univex function. In this paper we extend the concept of α -invexity [M.A. Noor, On generalized preinvex functions and monotonicities, J. Inequalities Pure Appl. Math. 5 (2004) 1–9] and pseudo α -invexity [S.K. Mishra, M.A. Noor, On vector variational-like inequality problems, J. Math. Anal. Appl. 311 (2005) 69–75] to α -univexity and pseudo α -univexity from a view point of generalized convexity. We also introduce the concept of strict pseudo α -univex and quasi α -univex 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 form of dual problems. The results in this paper extend a few known results in the literature.