{
  "abstract": "This paper focuses on difference-of-convex (DC) composite optimization problems with set-inclusion and manifold constraints. We develop an inexact proximal-linearized nonsmooth exact penalty (NEP) method that penalizes the conic constraint while retaining the manifold constraint explicitly. At each outer iteration, the method approximately solves a strongly convex proximal-linearized subproblem over the current tangent space, using computable inexactness criteria, adaptive parameters, and a retraction-based acceptance mechanism. Under boundedness of the iterates and penalty parameters, we establish an $O(ε^{-2})$ worst-case outer iteration complexity for finding an $ε$-approximate KKT point of the original problem. We further develop a complexity-transfer framework relating uniform primal objective-gap and KKT-residual decay, or dual objective-gap decay, to total inner-iteration complexity bounds. This yields an $O(ε^{-4})$ overall oracle complexity with either accelerated semi-proximal ADMM or FISTA applied to the dual subproblem as the inner solver. Using semi-proximal ADMM as the inner solver improves the bound to $O(ε^{-2}\\log(1/ε))$ under an additional uniform error-bound condition. We further establish convergence of the entire iterate sequence to a KKT point under the same boundedness assumption and the Kurdyka-Lojasiewicz property of the associated potential function. Numerical experiments demonstrate the competitive performance of the proposed method on row-sparse PCA, clustering, robust SVMs, and nonconvex SOCPs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14564",
  "author_total": 3,
  "authors": [
    {
      "name": "Hao He"
    },
    {
      "name": "Ruyu Liu"
    },
    {
      "name": "Shaohua Pan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9nmq7kvrhrdmk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14564",
  "fulltext_url": null,
  "id": "9nmq7kvrhrdmk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14564",
  "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",
      "1703|Optimization and Variational Analysis"
    ]
  ],
  "openalex": "W7213288879",
  "pdf_url": "https://arxiv.org/pdf/2609.14564",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9nmq7kvrhrdmk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2609.14564",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14564"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Proximal-Linearized NEP Method for Composite Optimization with Set-Inclusion and Manifold Constraints",
  "title_text": "Proximal-Linearized NEP Method for Composite Optimization with Set-Inclusion and Manifold Constraints",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/9nmq7kvrhrdmk",
  "venue": "arXiv",
  "versions": []
}