Summary: This paper considers the problem of maximizing a differentiable concave function subject to bound constraints and a Lipschitz condition on the gradient, using active set strategies. We introduce a general model algorithm for this class of problems. The algorithm includes a procedure for deciding to leave a face of the polytope without having reached a stationary point relative to that face but guaranteeing that return is not possible. We prove a global convergence result. Among the many possible applications, we suggest using our algorithm for optimization of external penalization functions on linear programming problems. Some numerical experiments concerning this application are presented.