{
  "abstract": "We study nonsmooth composite optimization over embedded submanifolds defined by nonlinear equality constraints. We propose a feasibility-safeguarded inexact proximal linearized method whose iterations require neither projection nor retraction onto the manifold. A computable smooth-dual residual certifies the approximate tangential step and controls the errors in both tangency and composite linearization consistency. The step is followed by a normal correction evaluated at the displaced trial point. To coordinate the resulting optimality and feasibility errors, a nonmonotone backtracking procedure reduces the tangential stepsize faster than the normal stepsize and accepts only corrected points within a prescribed constraint-violation region. Under the stated regularity and level-boundedness assumptions, we establish a uniform backtracking bound, positive lower bounds on the accepted stepsizes, boundedness of the primal and multiplier sequences, stationarity of all cluster points, and an $O(\\varepsilon^{-2})$ outer iteration complexity bound. The analysis does not assume compactness of the manifold or a separate global distance-to-manifold error bound. For a specified parameter regime guaranteeing full tangential steps, a KL assumption on an auxiliary function yields full-sequence convergence. Numerical experiments on sparse principal component analysis and sparse spectral clustering illustrate the performance of the method.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.24954",
  "author_total": 2,
  "authors": [
    {
      "name": "Xiyua Xie"
    },
    {
      "name": "Qia Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6y2qxnjc7a4ev.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.24954",
  "fulltext_url": null,
  "id": "6y2qxnjc7a4ev",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.24954",
  "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",
      "1703|Optimization and Variational Analysis"
    ]
  ],
  "openalex": "W7162427350",
  "pdf_url": "https://arxiv.org/pdf/2605.24954",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6y2qxnjc7a4ev.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2605.24954",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.24954"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "An Infeasible Method with Feasibility Safeguard for Nonsmooth Composite Optimization Over Manifolds",
  "title_text": "An Infeasible Method with Feasibility Safeguard for Nonsmooth Composite Optimization Over Manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/6y2qxnjc7a4ev",
  "venue": "arXiv",
  "versions": []
}