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.

Submitted to the Proceedings of Domain Decomposition Methods in Science and Engineering XXIX