We consider the problem of construction of optimal experimental designs (approximate theory) on a compact subset X of Rd with nonempty interior, for a concave and Lipschitz diff erentiable design criterion Phi (.) based on the information matrix. The proposed algorithm combines (a) convex optimization for the determination of optimal weights on a support set, (b) sequential updating of this support using local optimization, and (c) finding new support candidates using properties of the directional derivative of Phi(.). The algorithm makes use of the compactness of X and relies on a fi nite grid Xl C X for checking optimality. By exploiting the Lipschitz continuity of the directional derivatives of Phi(.), effi ciency bounds on X are obtained and epsilon-optimality on X is guaranteed. The eff ectiveness of the method is illustrated on a series of examples.