{
  "abstract": "We consider the minimization of a smooth function subject to box constraints and partitioned cardinality constraints (PCC): the variables are divided into groups and, within each group, at most a prescribed number of variables may be non-zero. This class contains bound-constrained minimization, cardinality-constrained minimization and bound-constrained mathematical programs with complementarity constraints. We introduce the Telescopic Method, which alternates iterations of a bound-constrained method on the faces of the feasible set with inexpensive one-dimensional \"escaping\" tests that exchange a variable of the current face by a currently null one within the same group. We prove, without constraint qualifications and without requiring global solutions of subproblems, that every limit point of the generated sequence is B-stationary, i.e., it satisfies the first-order condition defined by the tangent cone of the feasible set. This guarantee is obtained with exchanges of a single variable, whatever the number of non-null entries of the limit point, because B-stationarity for this class of problems decomposes into conditions on single variables. On the 60 bound-constrained mathematical programs with complementarity constraints of the test set of Kirches, Larson, Leyffer and Manns, the method found approximately B-stationary points in all the problems. Applications to separable regression, sparse polynomial approximation and portfolio selection are described and tested numerically.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00897",
  "author_total": 2,
  "authors": [
    {
      "name": "Ernesto G. Birgin"
    },
    {
      "name": "J. M. Martínez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7aafd9w81f55m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00897",
  "fulltext_url": null,
  "id": "7aafd9w81f55m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00897",
  "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/2611.00897",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7aafd9w81f55m.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00897",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00897"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A Telescopic Method with Guaranteed B-Stationarity for Partitioned Cardinality and Complementarity Constraints",
  "title_text": "A Telescopic Method with Guaranteed B-Stationarity for Partitioned Cardinality and Complementarity Constraints",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/7aafd9w81f55m",
  "venue": "arXiv",
  "versions": []
}