On Managing the Use of Surrogates in General Nonlinear Optimization and MDO

This paper is concerned with a trust-region approximation management framework (AMF) for solving the nonlinear programming problem, in general, and multidisciplinary optimization problems, in particular. The intent of the AMF methodology is to facilitate the solution of optimization problems with high-fidelity models. While such models are designed to approximate the physical phenomena they describe to a high degree of accuracy, they use in a repetitive procedure, for example, iterations of an optimization or a search algorithm, make such use prohabitively expensive. An improvement in design with lower-fidelity, cheaper models, however, does not guarantee a corresponding improvement for the higher-fidelity problem. The AMF methdology proposed here is based on a class of multilevel methods for constrained optimization and is designed to manage the use of variable-fidelity approximations or models in a systematic way that assures convergence to critical points of the original, high-fidelity problem.