Minimax fractional programming problem involving nonsmooth generalized ?-univex functions

In this paper, we introduce a new class of generalized α-univex functions where the involved functions are locally Lipschitz. We extend the concept of α-type I invex [S. K. Mishra, J. S. Rautela, On nondifferentiable minimax fractional programming under generalized α-type I invexity, J. Appl. Math. Comput. 31 (2009) 317-334] to α-univexity and an example is provided to show that there exist functions that are α-univex but not α-type I invex. Furthermore, Karush-Kuhn-Tucker-type sufficient optimality conditions and duality results for three different types of dual models are obtained for nondifferentiable minimax fractional programming problem involving generalized α-univex functions. The results in this paper extend some known results in the literature.