Abstract. In this paper we analyze the outer approximation property of the algorithm for generalized semi-infinite programming from O. Stein, G. Still, Solving semi-infinite optimization problems with interior point techniques. A simple bound on the regularization error is found and used to formulate a feasible numerical method for generalized semi-infinite programming with convex lower level problems. That is, all iterates of the numerical method are feasible points of the original optimization problem. The new method has the same computational cost as the original algorithm. We also discuss the merits of this approach for the adaptive convexification algorithm, a feasible point method for standard semi-infinite programming from C.A. Floudas, O. Stein, The adaptive convexification algorithm: a feasible point method for semi-infinite programming.