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arXiv · 2511.00434

Trust-Region Methods with Low-Fidelity Objective Models

Andrea Angino·Matteo Aurina·Alena Kopaničáková·Matthias Voigt·Marco Donatelli·Rolf Krause
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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.

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Andrea Angino, Matteo Aurina, Alena Kopaničáková, Matthias Voigt, Marco Donatelli, Rolf Krause. 2025-11-01. Trust-Region Methods with Low-Fidelity Objective Models. https://arxiv.org/abs/2511.00434

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