{
  "abstract": "In this paper, we propose a variance-reduced stochastic quasi-Newton sequential quadratic constrained quadratic programming method (VR-QN-SQCQP) for finite-sum nonlinear optimization with equality and inequality constraints. Exact nonlinear-constraint Hessians are replaced entirely by safeguarded symmetric rank-one (SR1) curvature models built from first-order constraint gradients, while PAGE estimates the objective gradient and an exact \\(L_1\\) merit function provides globalization. Under explicit regularity, boundedness, relative QCQP-accuracy, and step-length assumptions, the analysis establishes almost-sure subsequential convergence to Karush--Kuhn--Tucker (KKT) points and, under stronger uniform step-length and error-control conditions, an expected \\(O(\\varepsilon^{-2})\\) outer-iteration bound for the squared KKT residual. A conditional local stability result also compares learned-curvature directions with their exact-Hessian counterparts. Numerical experiments compare VR-QN-SQCQP against Exact-SQCQP-PAGE on Sparse PCA using 253,680 CDC BRFSS 2015 observations and on a dense nonlinear benchmark. Over ten seeds, both methods converge in all Sparse PCA runs, while on the dense benchmark the proposed method converges in 10/10 runs versus 9/10 for the exact-Hessian variant. The proposed method performs zero exact constraint-Hessian evaluations and reduces median curvature-construction time on the dense benchmark from 0.1230 s to 0.0111 s. Overall runtime benefits remain problem-dependent.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04403",
  "author_total": 2,
  "authors": [
    {
      "name": "Gopal Tiwari"
    },
    {
      "name": "Md Abu Talhamainuddin Ansary"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7v4sstdt5nfty.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04403",
  "fulltext_url": null,
  "id": "7v4sstdt5nfty",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04403",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04403",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7v4sstdt5nfty.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04403",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04403"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Variance-Reduced Stochastic Quasi-Newton SQCQP Method for Nonlinear Programming Problems",
  "title_text": "Variance-Reduced Stochastic Quasi-Newton SQCQP Method for Nonlinear Programming Problems",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:29Z",
  "url": "https://research.draconitic.com/paper/7v4sstdt5nfty",
  "venue": "arXiv",
  "versions": []
}