{
  "abstract": "We combine CaCuTe with sequential subspace optimization (SESOP) for smooth convex minimization under Lipschitz continuity of the Hessian. The resulting method, CaCuSESOP, achieves the global rate $O(k^{-2})$ with a fixed number of Hessian--vector products per iteration, while removing key limitations of classical SESOP. In particular, exact minimization of the original objective is replaced by minimization of a low-dimensional cubic upper model, which needs only be solved to a computable accuracy. The cubic regularization parameter is selected by backtracking. If the Hessian at the minimizer is positive definite, CaCuSESOP automatically attains an accelerated local linear rate with complexity $O(\\sqrt{κ_\\star}\\log(1/\\varepsilon))$. Neither the local strong-convexity parameter, the condition number $κ_\\star$, nor the optimal value is supplied to the algorithm. We give finite bounds for entering this regime and adapting the restart schedule. Finally, we prove that the global $O(k^{-2})$ rate is optimal for the considered fixed-budget gradient/Hessian--vector-product linear-span oracle class, even with momentum and unrestricted memory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06557",
  "author_total": 1,
  "authors": [
    {
      "name": "Nazarii Tupitsa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4vmnah7bch9ky.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06557",
  "fulltext_url": null,
  "id": "4vmnah7bch9ky",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06557",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7220710849",
  "pdf_url": "https://arxiv.org/pdf/2610.06557",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4vmnah7bch9ky.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.06557",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06557"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "CaCuTe Meets SESOP: Better Theory and Practice with Lipschitz Hessians",
  "title_text": "CaCuTe Meets SESOP: Better Theory and Practice with Lipschitz Hessians",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/4vmnah7bch9ky",
  "venue": "arXiv",
  "versions": []
}