{
  "abstract": "We develop an infeasible-start extension of the Topkis--Veinott feasible-direction method for nonconvex composite optimization. At each main iteration, a strongly convex local model is used to obtain objective descent while limiting increases in constraint violation. A separate feasibility-reduction step is invoked when feasibility improvement is needed. Under a feasibility-reduction condition, we establish the standard first-order rate for reducing the Fritz John residual and constraint violation. We then verify that both proximal-gradient and regularized Gauss--Newton methods applied to minimizing the squared constraint-violation function satisfy the required feasibility-reduction property under a Polyak--Łojasiewicz condition. Numerical experiments compare the reduction methods, including an experimental prox-linear variant, and compare the scalar-regularized and curvature-enhanced subproblem formulations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38842",
  "author_total": 2,
  "authors": [
    {
      "name": "Danlin Li"
    },
    {
      "name": "Johannes Milz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1195rj05vvxfc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38842",
  "fulltext_url": null,
  "id": "1195rj05vvxfc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38842",
  "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/2610.38842",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1195rj05vvxfc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38842",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38842"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A Feasible-Direction-Type Method for Nonconvex Optimization with Infeasible Starts",
  "title_text": "A Feasible-Direction-Type Method for Nonconvex Optimization with Infeasible Starts",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/1195rj05vvxfc",
  "venue": "arXiv",
  "versions": []
}