Mixed duality without a constraint qualification for minimax fractional programming

Without the need of a constraint qualification. we establish the necessary and sufficient optimality conditions for minimax fractional programming. Using these optimality conditions, we construct a mixed dual model which unifies the Mond-Weir dual, Wolfe dual and a parameter dual models. Several duality theorems are established. Consequently, this article partly solves the problem posed by Lai et al. [H.C. Lai, J.C. Liu and K. Tanaka (1999). Duality without a constraint qualification for minimax fractional programming. Journal of Optimization Theory and Applications, 101, 109-125.].