Error Analysis of Surrogate Models Constructed Through Operations on Submodels

Model-based methods are popular in derivative-free optimization (DFO). In most of them, a single model function is built to approximate the objective function. This is generally based on the assumption that the objective function is one black box. However, some real-life and theoretical problems show that the objective function may consist of sev-eral black boxes. In those problems, the information provided by each black box may not be equal. In this situation, one can build multiple submodels that are then combined to become a final model. In this paper, we analyze the relation between the accuracy of those submo-dels and the model constructed through their operations. We develop a broad framework that can be used as a theoretical tool in model error analysis and future research in DFO algorithm design.