Trust-Region Methods with Low-Fidelity Objective Models

TL;DR

This paper presents two novel multifidelity trust-region methods that leverage low-fidelity models to efficiently guide optimization, reducing computational cost while maintaining accuracy.

Contribution

The paper introduces Sketched Trust-Region and SVD Trust-Region methods that incorporate low-fidelity models into trust-region frameworks using innovative dimensionality reduction techniques.

Findings

Both methods demonstrate improved efficiency in numerical experiments.

The approaches effectively utilize low-fidelity models to accelerate convergence.

Numerical results show potential for significant computational savings.

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.