On nondifferentiable minimax fractional programmingunder generalized α-type I invexity

摘要

In this paper, we study a nondifferentiable minimax fractional program-ming problem under the assumptions of generalized α-type I invex function. In thispaper we introduce the concepts of α-type I invex, pseudo α-type I invex, strictpseudo α-type I invex and quasi α-type I invex functions in the setting of Clarkesubdifferential functions. We derive Karush-Kuhn-Tucker type sufficient optimalityconditions and establish weak, strong and converse duality theorems for the problemand its three different dual problems. The results in this paper extend several knownresults in the literature.