In the paper we show that if the quasi-convex function   defined on an open convex set satisfies some mild restrictions then   is a convex function on a convex compact subset if only C is larg e enough. We investigate specidly the casa when   separable, i.e. when  . Our results make possible the application of the methods of FIACCO and MCCORMICK in non-linear programming problems, where the constraints are quasi-convex.