{
  "abstract": "Both generalized absolute value equations (GAVEs) and linear complementarity problems (LCPs) can be formulated as least-squares problems over the complementarity set. Because this feasible set is nonconvex, projected stationarity does not in general imply zero residual. We develop a safeguarded projected-gradient framework with a linear-system refinement on a selected polyhedral face. We establish matrix conditions under which every projected stationary point is a global solution and derive corresponding global convergence results. Specifically, when refinement on a correct active face returns a solution, we give explicit iteration bounds for active-face identification and prove finite termination. Numerical experiments on GAVE and LCP benchmarks demonstrate the high accuracy of the proposed framework across the tested settings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.20786",
  "author_total": 3,
  "authors": [
    {
      "name": "Lianghai Xiao"
    },
    {
      "name": "Wei Zhang"
    },
    {
      "name": "Jiayi Zhong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/01d0v6qmmk8ra.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.20786",
  "fulltext_url": null,
  "id": "01d0v6qmmk8ra",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.20786",
  "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",
      "2612|Advanced Optimization Algorithms Research"
    ]
  ],
  "openalex": "W7170497229",
  "pdf_url": "https://arxiv.org/pdf/2607.20786",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/01d0v6qmmk8ra.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2607.20786",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.20786"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A Safeguarded Projected-Gradient Framework for Complementarity Constrained Least Squares Problems",
  "title_text": "A Safeguarded Projected-Gradient Framework for Complementarity Constrained Least Squares Problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/01d0v6qmmk8ra",
  "venue": "arXiv",
  "versions": []
}