# Linear-programming duality

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

[Catalogue presentation and source-binding data](https://ocme.evemisslab.com/data/i18n/catalogue.en.json)



## [Linear-programming duality](https://ocme.evemisslab.com/en/atlas/atlas-linear-program-duality/)

For primal maximize c^T*x with A*x≤b,x≥0, the dual minimizes b^T*y with A^T*y≥c,y≥0; feasible pairs satisfy weak duality.

atlas-linear-program-duality · canonical_mko

[Linear-programming duality](https://ocme.evemisslab.com/en/mko/mko-linear-program-duality/)

## Prerequisite nodes


- [Standard form of a linear program](https://ocme.evemisslab.com/en/atlas/atlas-linear-program-standard-form/)
- [Optimization problem](https://ocme.evemisslab.com/en/atlas/atlas-optimization-problem/)
- [Usual order on the real numbers](https://ocme.evemisslab.com/en/atlas/atlas-order-relation/)