{
  "abstract": "Second-order cone programs (SOCPs) are a fundamental class of convex optimization problems widely applied across engineering domains. Classical interior-point methods are robust and accurate, but their iterative nature can be costly in real-time or repeated-solve settings. This has motivated learning-based solvers that approximate optimizer solutions with neural networks. Recent work has increasingly studied graph neural networks (GNNs) for linear, quadratic, and second-order cone optimization, leveraging their ability to model sparse relational structure among variables, constraints, and objective functions. Most existing GNN-based solvers compress the optimization process into a single forward pass, predicting the optimizer directly without using the intermediate trajectory produced by classical solvers. We introduce SOCPNet, a recursive GNN framework that uses solver trajectories to learn an iterative SOCP solution procedure. A shared GNN model is applied repeatedly, refining the current iterate at each step and enabling inference for a variable number of iterations. Rather than predicting the solution in a single pass, SOCPNet learns from intermediate iterates to progressively refine its estimates using a trajectory-regularized training procedure. We evaluate SOCPNet on multiple datasets spanning standard SOCP problem classes and show that it consistently reduces the final solution error relative to a SOCP-GNN baseline. Finally, we demonstrate how trained SOCPNet models can be used in a hybrid optimization pipeline by warm-starting a classical interior-point solver, reducing solver iterations without loss of accuracy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26285",
  "author_total": 4,
  "authors": [
    {
      "name": "Adam Ghalem"
    },
    {
      "name": "Lou Salaün"
    },
    {
      "name": "Davide Rinaldi"
    },
    {
      "name": "Fragkiskos D. Malliaros"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/87a5kwzkr28b1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26285",
  "fulltext_url": null,
  "id": "87a5kwzkr28b1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26285",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2612|Advanced Optimization Algorithms Research"
    ]
  ],
  "openalex": "W7223069860",
  "pdf_url": "https://arxiv.org/pdf/2610.26285",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/87a5kwzkr28b1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.26285",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26285"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Learning SOCP Solver Dynamics with Graph Neural Networks",
  "title_text": "Learning SOCP Solver Dynamics with Graph Neural Networks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/87a5kwzkr28b1",
  "venue": "arXiv",
  "versions": []
}