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 X of R d with nonempty interior, for a concave and Lipschitz differentiable design criterion ϕ ( · ) 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 ϕ ( · ) . The algorithm makes use of the compactness of X and relies on a finite grid X ℓ ⊂ X for checking optimality. By exploiting the Lipschitz continuity of the directional derivatives of ϕ ( · ) , efficiency bounds on X are obtained and ϵ-optimality on X is guaranteed. The effectiveness of the method is illustrated on a series of examples.