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A Telescopic Method with Guaranteed B-Stationarity for Partitioned Cardinality and Complementarity Constraints — arXiv:2611.00897

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.00897
License (as archived): CC0-1.0
Archived: 2026-11-03T11:31:37.542Z
SHA-256 of the archived text: e6c6058398127e56c1f00eecac3f2597d6ac89a75e4234d6199698f5a4df8a23
Stable URL of this page: https://metraipolis.com/documento/dc_7fa6567c90cb

How to cite

A Telescopic Method with Guaranteed B-Stationarity for Partitioned Cardinality and Complementarity Constraints — arXiv:2611.00897 — arXiv (en), https://arxiv.org/abs/2611.00897 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_7fa6567c90cb (Metraipolis archive dc_7fa6567c90cb, sha256 e6c6058398127e56c1f00eecac3f2597d6ac89a75e4234d6199698f5a4df8a23)

BibTeX

@misc{dc7fa6567c90cb,
  title = {A Telescopic Method with Guaranteed B-Stationarity for Partitioned Cardinality and Complementarity Constraints — arXiv:2611.00897},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.00897},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_7fa6567c90cb; sha256 e6c6058398127e56c1f00eecac3f2597d6ac89a75e4234d6199698f5a4df8a23},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.00897. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.OC, nuovi lavori del giorno).
Categorie arXiv: Optimization and Control (math.OC).
Pagina del lavoro: https://arxiv.org/abs/2611.00897 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T11:04:22.213Z dalla pagina https://arxiv.org/list/math.OC/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).