AI engineering glossary · Calculus optimisation
What is lagrange multiplier?
Lagrange multiplier (also called Method of Lagrange multipliers): A number attached to a constraint that converts a constrained problem into an unconstrained one via the Lagrangian. At the solution it measures how sensitive the optimal value is to loosening that constraint.
Lagrange multiplier: an example
To minimise x^2 + y^2 subject to x + y = 2, set gradient f = lambda * gradient of constraint: 2x = lambda and 2y = lambda, so x = y = 1 and lambda = 2.
Related terms
More Calculus optimisation terms
- Lagrangian
- Learning rate
- Learning rate schedule
- Learning rate warmup
- Level set
- Levenberg-Marquardt algorithm
- Limit
- Line search
Where you learn it
Lagrange multiplier is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.