{
  "abstract": "This paper introduces a hybrid joint-selective optimization (HJSO) framework for large-scale numerical problems in which a small subset of trainable quantities is of primary interest. We partition the full parameter vector into a high-dimensional remaining block and a low-dimensional block of parameters of interest (POIs), perform joint first-order optimization over the full parameter set, and then freeze the remaining variables while applying a reduced-space Levenberg-Marquardt (LM) refinement to the POIs. The method is designed for settings in which the POIs are low-dimensional but strongly influence the quality of the computed solution, while the full parameter space remains too large for full-space second-order methods. The framework is evaluated on three representative problems: a matrix eigenvalue problem, an inverse Bratu problem solved with a physics-informed neural network, and a 100-dimensional nonlinear Black-Scholes problem solved with the DeepBSDE method. In each test, HJSO reaches prescribed POI-error thresholds faster than the corresponding joint first-order baseline and improves the final POI accuracy for the reported solver configurations. The contribution is therefore not a universal optimizer, but a practical reduced-space strategy for problems with known low-dimensional parameters of interest and expensive high-dimensional training variables.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37308",
  "author_total": 4,
  "authors": [
    {
      "name": "Muhammad Luthfi Shahab"
    },
    {
      "name": "Gabriella Alfa Indahsari"
    },
    {
      "name": "Imam Mukhlash"
    },
    {
      "name": "Hadi Susanto"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9v7nrednt8yvd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37308",
  "fulltext_url": null,
  "id": "9v7nrednt8yvd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37308",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "cs.NE"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.37308",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9v7nrednt8yvd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37308",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37308"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Hybrid Joint-Selective Optimization: Reduced-Space Levenberg-Marquardt Refinement of Low-Dimensional Parameters of Interest",
  "title_text": "Hybrid Joint-Selective Optimization: Reduced-Space Levenberg-Marquardt Refinement of Low-Dimensional Parameters of Interest",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/9v7nrednt8yvd",
  "venue": "arXiv",
  "versions": []
}