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