AI engineering glossary · Calculus optimisation
What is lagrangian?
Lagrangian: The function formed by adding each constraint, multiplied by its multiplier, to the objective: L(x, lambda) = f(x) + lambda * g(x). Its stationary points give candidate constrained optima and it is the starting point for duality.
Lagrangian: an example
For f = x^2 + y^2 and constraint x + y - 2 = 0, L = x^2 + y^2 + lambda * (x + y - 2).
Related terms
More Calculus optimisation terms
- Learning rate
- Learning rate schedule
- Learning rate warmup
- Level set
- Levenberg-Marquardt algorithm
- Limit
- Line search
- Linear approximation
Where you learn it
Lagrangian is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.