{
  "abstract": "We study difference-of-convex optimization problems with several composite inequality constraints and develop a majorization-guided switching proximal gradient (MGSPG) method. Specifically, at each feasible outer point, quadratic majorization and linearization yield a strongly convex composite surrogate problem. To solve this surrogate approximately, we employ a switching proximal gradient (SPG) method, which takes a proximal gradient step for the objective when the current point is nearly feasible and for a most violated constraint otherwise. This construction requires neither projection onto the joint surrogate feasible set nor multiplier computation. By establishing a common invariant ball and using an increasing weight argument, we obtain an \\(O(τ^{-1})\\) inner complexity bound for SPG. Building on this bound, we show that, under boundedness of the feasible level set and a uniform Slater condition for the surrogates, MGSPG finds an \\(\\varepsilon\\)-KKT point in \\(O(\\varepsilon^{-2})\\) outer iterations and \\(O(\\varepsilon^{-4})\\) selected component proximal gradient updates. Numerical experiments on SCAD-constrained and groupwise-constrained regression problems demonstrate the viability and computational efficiency of our method compared with existing optimization algorithms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37362",
  "author_total": 3,
  "authors": [
    {
      "name": "Yuncheng Liu"
    },
    {
      "name": "Chuangliang Zhang"
    },
    {
      "name": "Bo Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e3m1x07ac50m2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37362",
  "fulltext_url": null,
  "id": "e3m1x07ac50m2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37362",
  "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": "W7224092708",
  "pdf_url": "https://arxiv.org/pdf/2610.37362",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e3m1x07ac50m2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37362",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37362"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A switching proximal gradient method for constrained difference-of-convex optimization problems",
  "title_text": "A switching proximal gradient method for constrained difference-of-convex optimization problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/e3m1x07ac50m2",
  "venue": "arXiv",
  "versions": []
}