Minimax Fractional Programming for n-Set Functions and Mixed-Type Duality under Generalized Invexity

We establish the sufficient optimality conditions for a minimax programming problem involving p fractional n-set functions under generalized invexity. Using incomplete Lagrange duality, we formulate a mixed-type dual problem which unifies the Wolfe type dual and Mond-Weir type dual in fractional n-set functions under generalized invexity. Furthermore, we establish three duality theorems: weak, strong, and strict converse duality theorem, and prove that the optimal values of the primal problem and the mixed-type dual problem have no duality gap under extra assumptions in the framework.