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Non-negative least squares — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Non-negative_least_squares
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-15T19:16:18.932Z
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Non-negative least squares — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Non-negative_least_squares (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_2dcfcd154014 (Metraipolis archive dc_2dcfcd154014, sha256 ee0d32991d5f5815c1bd37ea4119c9559f3b7400342b922fd2ced9d163dd131f)

BibTeX

@misc{dc2dcfcd154014,
  title = {Non-negative least squares — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Non-negative_least_squares},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_2dcfcd154014; sha256 ee0d32991d5f5815c1bd37ea4119c9559f3b7400342b922fd2ced9d163dd131f},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Non-negative_least_squares. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In mathematical optimization, the problem of non-negative least squares (NNLS) is a type of constrained least squares problem where the coefficients are not allowed to become negative. That is, given a matrix A and a (column) vector of response variables y, the goal is to find a r g m i n x ‖ A x − y ‖ 2 2 {\displaystyle \operatorname {arg\,min} \limits _{\mathbf {x} }\|\mathbf {Ax} -\mathbf {y} \|_{2}^{2}} subject to x ≥ 0. Here x ≥ 0 means that each component of the vector x should be non-negative, and ‖·‖2 denotes the Euclidean norm. Non-negative least squares problems turn up as subproblems in matrix decomposition, e.g. in algorithms for PARAFAC and non-negative matrix/tensor factorization. The latter can be considered a generalization of NNLS. Another generalization of NNLS is bounded-variable least squares (BVLS), with simultaneous upper and lower bounds αi ≤ xi ≤ βi.

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; ricerca «mathematical optimization»).
Fonte: Wikipedia in inglese, voce «Non-negative least squares» — https://en.wikipedia.org/wiki/Non-negative_least_squares
Wikidata Q17086437: «constrained least squares problem» (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q17086437
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Non-negative_least_squares?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1368876172, consultata il 2026-10-15T18:31:01.712Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 39bc94f9045e2eb8ef809787d9343b39ec4566027a024b8e8eb0140972a4e6ef