# Necessary Lagrange multiplier condition for equality constraints

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)



## [Necessary Lagrange multiplier condition for equality constraints](https://ocme.evemisslab.com/en/atlas/atlas-lagrange-multiplier-condition/)

At a regular feasible constrained local extremum, the objective gradient is a linear combination of the constraint gradients.

atlas-lagrange-multiplier-condition · canonical_mko

[Necessary Lagrange multiplier condition for equality constraints](https://ocme.evemisslab.com/en/mko/mko-lagrange-multiplier-condition/)

## Prerequisite nodes


- [Gradient vector](https://ocme.evemisslab.com/en/atlas/atlas-gradient-vector/)
- [Optimization problem](https://ocme.evemisslab.com/en/atlas/atlas-optimization-problem/)
- [Linear systems in two variables and degenerate constraints](https://ocme.evemisslab.com/en/atlas/atlas-system-linear-equations/)
- [Matrix rank](https://ocme.evemisslab.com/en/atlas/atlas-matrix-rank/)
- [Linear independence and bases](https://ocme.evemisslab.com/en/atlas/atlas-linear-independence-basis/)