  Algorithms which compute locally optimal continuous designs often rely on a
finite design space or on repeatedly solving a complex non-linear program. Both
methods require extensive evaluations of the Jacobian Df of the underlying
model. These evaluations present a heavy computational burden. Based on the
Kiefer-Wolfowitz Equivalence Theorem we present a novel design of experiments
algorithm which computes optimal designs in a continuous design space. For this
iterative algorithm we combine an adaptive Bayes-like sampling scheme with
Gaussian process regression to approximate the directional derivative of the
design criterion. The approximation allows us to adaptively select new design
points on which to evaluate the model. The adaptive selection of the algorithm
requires significantly less evaluations of Df and reduces the runtime of the
computations. We show the viability of the new algorithm on two examples from
chemical engineering.
