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Benders decomposition — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Benders_decomposition
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-07T17:33:24.007Z
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Benders decomposition — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Benders_decomposition (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_caa95add3db2 (Metraipolis archive dc_caa95add3db2, sha256 c7926096b0e79db779a1f58ee7f7848837dbbc09b04c56429566fca629cc1cf1)

BibTeX

@misc{dccaa95add3db2,
  title = {Benders decomposition — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Benders_decomposition},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_caa95add3db2; sha256 c7926096b0e79db779a1f58ee7f7848837dbbc09b04c56429566fca629cc1cf1},
  year = {2026}
}

Archived text

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

Benders decomposition (or Benders' decomposition) is a technique in mathematical optimization that allows the solution of very large linear programming problems that have a special block structure. This block structure often occurs in applications such as stochastic programming as the uncertainty is usually represented with scenarios. The technique is named after Jacques F. Benders. The strategy behind Benders decomposition can be summarized as divide-and-conquer. That is, in Benders decomposition, the variables of the original problem are divided into two subsets so that a first-stage master problem is solved over the first set of variables, and the values for the second set of variables are determined in a second-stage subproblem for a given first-stage solution. If the subproblem determines that the fixed first-stage decisions are in fact infeasible, then so-called Benders cuts are generated and added to the master problem, which is then re-solved until no cuts can be generated. Since Benders decomposition adds new constraints as it progresses towards a solution, the approach is called "row generation". In contrast, Dantzig–Wolfe decomposition uses "column generation".

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; ricerca «mathematical optimization»).
Fonte: Wikipedia in inglese, voce «Benders decomposition» — https://en.wikipedia.org/wiki/Benders_decomposition
Wikidata Q3042795 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q3042795
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Benders_decomposition?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 1362575855, consultata il 2026-10-07T17:03:35.239Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 9e69e7d153eb5e18cb530f332ad179315b4276c49971fbebf7016d31f49e4dc8