{"ID":2847201,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.00434","arxiv_id":"2511.00434","title":"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.","short_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-fide...","url_abs":"https://arxiv.org/abs/2511.00434","url_pdf":"https://arxiv.org/pdf/2511.00434v1","authors":"[\"Andrea Angino\",\"Matteo Aurina\",\"Alena Kopaničáková\",\"Matthias Voigt\",\"Marco Donatelli\",\"Rolf Krause\"]","published":"2025-11-01T07:25:43Z","proceeding":"math.NA","tasks":"[\"math.NA\",\"cs.LG\",\"stat.ML\"]","methods":"[]","has_code":false}