Minimax fractional programming problem involving nonsmooth generalized ?-univex functions

Abstract

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