{
  "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 first-order 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). A similarly refined analysis of the analogous second-order subspace method from [Cartis & Roberts, Opt. Meth. & Softw. (2026)] shows that using suitably scaled JLTs to generate the subspaces gives a better complexity bound, which improves over full-space methods only if the problem has low effective rank.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.17307",
  "author_total": 2,
  "authors": [
    {
      "name": "Coralia Cartis"
    },
    {
      "name": "Lindon Roberts"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d5bw2gayyj4j3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.17307",
  "fulltext_url": null,
  "id": "d5bw2gayyj4j3",
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  "landing_url": "https://arxiv.org/abs/2608.17307",
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  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
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      "openalex",
      "2612|Advanced Optimization Algorithms Research"
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  "openalex": "W7203783899",
  "pdf_url": "https://arxiv.org/pdf/2608.17307",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d5bw2gayyj4j3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2608.17307",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.17307"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A note on the complexity of random subspace model-based methods for derivative-free optimization",
  "title_text": "A note on the complexity of random subspace model-based methods for derivative-free optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/d5bw2gayyj4j3",
  "venue": "arXiv",
  "versions": []
}