AI engineering glossary · Calculus optimisation
What is local minimum?
Local minimum: A point whose function value is lower than at every other point in a small neighbourhood, though a lower value may exist elsewhere. Gradient-based methods can settle there because the slope is zero.
Local minimum: an example
f(x) = x^4 - 3x^2 + x has a shallow local minimum near x = 1.13 and a deeper global minimum near x = -1.30.
Related terms
More Calculus optimisation terms
- Loss landscape
- Mini-batch gradient descent
- Momentum
- Multivariable chain rule
- Natural logarithm
- Nesterov momentum
- Newton's method
- Numerical differentiation
Where you learn it
Local minimum is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.