{
  "abstract": "In a predictor-corrector arc-search method, a point on the predictor arc is first selected and a corrector is then computed at that point. Since the Karush-Kuhn-Tucker (KKT) matrix changes with the selected point, this correction may require a second factorization in each iteration. We propose a one-factorization arc-search method (OFAS) for semidefinite programming (SDP) that avoids this second factorization, retains the corrector after the arc step, and uses only one KKT factorization per iteration. The key is a three-term decomposition of the complementarity mismatch at the selected point on the arc, which allows the correction to be assembled from linear-system solutions using the factorization at the current iterate. We also propose a curvature-amplified variant (CA-OFAS) that amplifies the second-order arc term. The proposed methods are formulated with a homogeneous self-dual embedding. For a wide long-step neighborhood, we prove that both methods reduce the homogeneous complementarity and residuals below $\\varepsilon$ in $O(n \\log(1/\\varepsilon))$ iterations for an $n$-by-$n$ SDP matrix variable. Numerical experiments show that the one-factorization structure and the correction after the arc step are associated with reductions in computation time. Compared with the Mehrotra-type method, CA-OFAS reduces the geometric-mean computation time by 17% on SDPLIB and 13% on neural network verification SDP problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34275",
  "author_total": 2,
  "authors": [
    {
      "name": "Makoto Yamashita"
    },
    {
      "name": "Yaguang Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/94s1z80pa87xy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34275",
  "fulltext_url": null,
  "id": "94s1z80pa87xy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34275",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2612|Advanced Optimization Algorithms Research"
    ]
  ],
  "openalex": "W7214722177",
  "pdf_url": "https://arxiv.org/pdf/2609.34275",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/94s1z80pa87xy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.34275",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34275"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A One-Factorization Predictor-Corrector Long-Step Arc-Search Method and a Curvature-Amplified Variant for Semidefinite Programming with a Homogeneous Self-Dual Embedding",
  "title_text": "A One-Factorization Predictor-Corrector Long-Step Arc-Search Method and a Curvature-Amplified Variant for Semidefinite Programming with a Homogeneous Self-Dual Embedding",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/94s1z80pa87xy",
  "venue": "arXiv",
  "versions": []
}