AI engineering glossary · Calculus optimisation
What is first-order condition?
First-order condition: The necessary requirement that the gradient of a differentiable function equals zero at an unconstrained optimum. It identifies candidate points but cannot by itself say whether each is a minimum, maximum or saddle.
First-order condition: an example
For f(x, y) = x^2 + y^2 - 4x, setting the gradient (2x - 4, 2y) to zero gives the candidate point (2, 0).
Related terms
More Calculus optimisation terms
- Flat minimum
- Forward-mode automatic differentiation
- Function
- Fundamental theorem of calculus
- Gauss-Newton method
- Genetic algorithm
- Global minimum
- Gradient
Where you learn it
First-order condition is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.