Trust-Region Methods with Low-Fidelity Objective Models
Abstract
We introduce two multifidelity trust-region methods based on the Magical Trust Region (MTR) framework. MTR augments the classical trust-region step with a secondary, informative direction. In our approaches, the secondary ``magical'' directions are determined by solving coarse trust-region subproblems based on low-fidelity objective models. The first proposed method, Sketched Trust-Region (STR), constructs this secondary direction using a sketched matrix to reduce the dimensionality of the trust-region subproblem. The second method, SVD Trust-Region (SVDTR), defines the magical direction via a truncated singular value decomposition of the dataset, capturing the leading directions of variability. Several numerical examples illustrate the potential gain in efficiency.
Cite
@article{arxiv.2511.00434,
title = {Trust-Region Methods with Low-Fidelity Objective Models},
author = {Andrea Angino and Matteo Aurina and Alena Kopaničáková and Matthias Voigt and Marco Donatelli and Rolf Krause},
journal= {arXiv preprint arXiv:2511.00434},
year = {2025}
}
Comments
Submitted to the Proceedings of Domain Decomposition Methods in Science and Engineering XXIX