{
  "abstract": "This paper studies finite-sum convex optimization with convex function constraints, where both the objective $f(x)=\\frac{1}{m}\\sum_{i=1}^m f_i(x)$ and the constraint mapping $g(x)=\\frac{1}{n}\\sum_{j=1}^n g_j(x)$ may have a large number of components. We propose a variance-reduced anchored constraint extrapolation method (VaRAn-ConEx), which combines stochastic component sampling with primal--dual extrapolation for nonlinear function constraints. Relative to stochastic approximation schemes such as ConEx, VaRAn-ConEx~method reduces gradient complexity by using epoch-wise full-gradient correction and variance-reduced estimators for both the objective and constraint components. In the semi-finite case where $n=1$, the method attains gradient complexities $O(\\sqrt m/ε)$ under constant steps and $O(m/ε^{1/2}+1/ε^{3/2})$ under nonconstant steps. In the fully finite-sum case, we establish boundedness of the Lagrange multiplier sequence and derive convergence and gradient-complexity bounds for constant and nonconstant step-size policies. Under these policies, we then prove similar gradient complexity with $m$ replaced by $\\max\\{m,n\\}$. We also show acceleration when the finite-sum objective $f$ is strongly convex, irrespective of components $f_i$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00317",
  "author_total": 2,
  "authors": [
    {
      "name": "Yasin Gharehmohammadlou"
    },
    {
      "name": "Digvijay Boob"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7w50e84zf51nd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00317",
  "fulltext_url": null,
  "id": "7w50e84zf51nd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00317",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00317",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7w50e84zf51nd.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00317",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00317"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Variance-reduced First-order Methods for Finite-sum Function Constrained Convex Optimization",
  "title_text": "Variance-reduced First-order Methods for Finite-sum Function Constrained Convex Optimization",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/7w50e84zf51nd",
  "venue": "arXiv",
  "versions": []
}