Boundedness of KKT Multipliers in Fractional Programming Problem Using Convexificators

Here, using the idea of convexificators, we study boundedness and nonemptiness of lagrange multipliers satisfying the first order necessary conditions. We consider a class of nonsmooth fractional programming problems with equality and inequality constraints and an arbitrary set constraint. Within this context, we define a generalized Mangasarian-Fromovitz type constraint qualification and show that this constraint qualification is necessary and sufficient conditions for the Karush-Kuhn-Tucker (KKT) multipliers set to be nonempty and bounded.