A note on the complexity of random subspace model-based methods for derivative-free optimization
Year: 2026
Type: preprint
Abstract: We demonstrate that, with a suitable rescaling, using Johnson-Lindenstrauss transforms (JLTs) in the random subspace model-based derivative-free optimization (DFO) algorithm from [Cartis & Roberts, Math. Prog. 199 (2023)] achieves an improved worst-case evaluation complexity bound compared to 'unscaled' JLTs. This improved bound does not require any modification to the original algorithm or complexity analysis, and matches the best-known bound in terms of dimension dependence for model-based DFO (e.g. achieved by [Scheinberg & Chaudhry, ICM 2026] using Haar matrices in a similar framework).
Source: arXiv (Cornell University)
Authors: Cartis, Coralia, Roberts, Lindon
Institutions: University of Oxford, The University of Melbourne
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203783899
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