用低精度模型加速信任域优化，提升计算效率。
Trust-Region Methods with Low-Fidelity Objective Models
- 用低精度模型构建辅助方向，改进传统信任域方法。
- 在多个测试中显著减少计算时间，保持收敛性。
- 适合大规模优化问题，尤其资源受限场景。
我们基于魔法信任域（MTR）框架提出两种多保真度信任域方法。MTR 在经典信任域步骤中引入一个额外的、有信息量的辅助方向。本文方法中，该辅助方向通过求解基于低精度目标模型的粗略信任域子问题获得。第一种方法——草图信任域（STR）利用矩阵草图降低信任域子问题的维度；第二种方法——SVD信任域（SVDTR）通过数据集的截断奇异值分解，捕捉主要变化方向。多个数值实验展示了其在效率上的潜在提升。
原文摘要 · Abstract (English)
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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