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

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 In this paper, we consider a multi-objective hub location problem (MOHLP) to locate two constrained    facilities in order to minimize the distance between these facilities and the weighted distance between each facility and related customers. For this purpose, we establish a necessary and sufficient condition of optimality for finding an efficient solution of the problem. We show that MOHLP can be reduced to a simple bi-level distance problem. Then we develop an efficient algorithm to find the optimal solution set of BDP,  and provide its convergence without any assumption. Moreover, an algorithm is proposed to solve MOHLP, which converges in a finite number of iterations. Some examples are stated to clarify the proposed algorithms.