{
  "abstract": "This manuscript studies a constraint dissolving method for solving optimization problems with general constraints, comprising an abstract constraint G(x) \\in C and a potentially nonconvex geometric constraint x \\in D, which, to the best of our knowledge, is the first constraint dissolving type method applicable to this general setting. More specifically, we introduce an auxiliary variable s to decouple G(x) \\in C into G(x) = s and s \\in C, and construct the constraint dissolving mapping acting jointly on both variables. We then propose a penalty-based constraint dissolving method, in which the penalty parameter is updated adaptively according to the feasibility error. Under mild conditions, every accumulation point is Mordukhovich-stationary. By a specific choice of the constraint dissolving mapping, every accumulation point is guaranteed to be feasible, which stands in contrast to standard penalty-type methods in nonconvex settings. Numerical experiments on Rosenbrock, portfolio, and MAXCUT problems demonstrate the effectiveness of the proposed method against the augmented Lagrangian and the penalty decomposition methods.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04954",
  "author_total": 3,
  "authors": [
    {
      "name": "Pengjie Liu"
    },
    {
      "name": "Haonan Shen"
    },
    {
      "name": "Xiaoxi Jia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c9fg8yxry4fpt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04954",
  "fulltext_url": null,
  "id": "c9fg8yxry4fpt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04954",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04954",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c9fg8yxry4fpt.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04954",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04954"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A constraint dissolving method for generally constrained optimization over a nonconvex set",
  "title_text": "A constraint dissolving method for generally constrained optimization over a nonconvex set",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/c9fg8yxry4fpt",
  "venue": "arXiv",
  "versions": []
}