{
  "abstract": "We study entropy-regularized linear programs with sparse affine constraints and compare two exact dual representations induced by whether a redundant normalization constraint is retained or eliminated. Eliminating it yields a partially separable sum-exp dual with sparse affine factors but unbounded curvature. Our main result is an accelerated randomized block method whose acceleration preserves sparse data-access cost. The key ingredient is a global entropy-specific Hessian--gap bound that remains valid for signed constraint matrices, admits computable block-overlap refinements, and provides deterministic curvature certificates before sampling. This geometry supports square-root importance sampling and an exact lazy implementation in which sparse arithmetic cost is weighted by local curvature rather than by a worst-block factor. We further introduce a gap-dependent curvature dimension that connects the generalized-smooth regime to the classical effective-rank intuition for coordinate methods. Retaining the normalization constraint yields a log-sum-exp dual with globally bounded higher derivatives, enabling gradient-regularized and cubic-regularized Newton methods. Experiments compare the resulting methods in terms of coordinate epochs, arithmetic operations, and wall-clock time, separating the effects of acceleration, touched-data sparsity, and problem-specific structure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32558",
  "author_total": 5,
  "authors": [
    {
      "name": "Irina Podlipnova"
    },
    {
      "name": "Maxim Mashtaler"
    },
    {
      "name": "Artem Agafonov"
    },
    {
      "name": "Yuriy Dorn"
    },
    {
      "name": "Alexander Gasnikov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bj6ys0gkefs9p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32558",
  "fulltext_url": null,
  "id": "bj6ys0gkefs9p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32558",
  "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": "W7214765225",
  "pdf_url": "https://arxiv.org/pdf/2609.32558",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bj6ys0gkefs9p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32558",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32558"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Smooth or Separable? Sparse Block Acceleration for Entropy-Regularized Linear Programs",
  "title_text": "Smooth or Separable? Sparse Block Acceleration for Entropy-Regularized Linear Programs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/bj6ys0gkefs9p",
  "venue": "arXiv",
  "versions": []
}