Adaptation of the Uobyqa Algorithm for Noisy Functions

In many real-world optimization problems, the objective function may come from a simulation evaluation so that it is (a) subject to various levels of noise, (b) not differentiable, and (c) computationally hard to evaluate. In this paper, we modify Powell's UOBYQA algorithm to handle those real-world simulation problems. Our modifications apply Bayesian techniques to guide appropriate sampling strategies to estimate the objective function. We aim to make the underlying UOBYQA algorithm proceed efficiently while simultaneously controlling the amount of computational effort