DAE

Abstract

Optimization of the output of computer simulators, whether deterministic or stochastic, is a challenging problem because of the typical severe multimodality. The problem is further complicated when the optimization is subject to unknown constraints, those that depend on the value of the output, so the function must be evaluated in order to determine if the constraint has been violated. Yet, even an invalid response may still be informative about the function, and thus could potentially be useful in the optimization. We develop a statistical approach based on Gaussian processes and Bayesian learning to approximate the unknown function and to estimate the probability of meeting the constraints, leading to a sequential design for optimization and calibration.