{
  "abstract": "First-order methods for linear conic programming often stall on long plateaus. Existing analyses characterize when during a run or on which problem instances slow convergence occurs; we instead ask where in the state space slow convergence is present. We introduce the slow region family for parameterized averaged fixed-point iterations. On a slow region, one step moves the state by only a small fraction of its distance to the fixed-point set, so an orbit starting there keeps almost its initial distance for arbitrarily many iterations. We then develop the afterimage principle to construct them. A center family and a nearby petal family share the same limit parameter, so their residual fields become close, while their fixed-point sets or forward drifts stay far apart. The petal geometry then certifies a slow region for the center. We verify the standing assumptions for ADMM, sGS-ADMM, and PDHG, and give an LP, SOCP, and SDP gallery showing how varied slow regions can be.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09449",
  "author_total": 2,
  "authors": [
    {
      "name": "Shucheng Kang"
    },
    {
      "name": "Heng Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cnzz1m4ppq1f0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09449",
  "fulltext_url": null,
  "id": "cnzz1m4ppq1f0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09449",
  "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",
      "1703|Optimization and Variational Analysis"
    ]
  ],
  "openalex": "W7212107840",
  "pdf_url": "https://arxiv.org/pdf/2609.09449",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cnzz1m4ppq1f0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.09449",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09449"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Afterimage Slow Regions in First-Order Methods for Linear Conic Programming",
  "title_text": "Afterimage Slow Regions in First-Order Methods for Linear Conic Programming",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/cnzz1m4ppq1f0",
  "venue": "arXiv",
  "versions": []
}