Trust-Region Methods with Low-Fidelity Objective Models
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Abstract (arXiv)
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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References · 5
- 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
- 2018Survey of multifidelity methods in uncertainty propagation, inference, and optimizationcited by 142
- 2015Newton Sketch: A Linear-time Optimization Algorithm with Linear-Quadratic Convergencecited by 72
- 2020A stochastic subspace approach to gradient-free optimization in high dimensionscited by 16
- 2022Randomised subspace methods for non-convex optimization, with applications to nonlinear least-squarescited by 4
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