Algorithmic construction of optimal designs on compact sets for concave and differentiable criteria

We consider the problem of construction of optimal experimental designs (approximate theory) on a compact subset chi of R-d with nonempty interior, for a concave and Lipschitz differentiable 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 chi and relies on a finite grid chi(l) subset of chi for checking optimality. By exploiting the Lipschitz continuity of the directional derivatives of phi(.), efficiency bounds on chi are obtained and epsilon-optimality on chi is guaranteed. The effectiveness of the method is illustrated on a series of examples. (C) 2014 Elsevier B.V. All rights reserved.