AI engineering glossary · Calculus optimisation
What is second-order condition?
Second-order condition: A test using the Hessian at a stationary point: if it is positive definite (all eigenvalues positive) the point is a strict local minimum, if negative definite a local maximum, and if it has mixed signs a saddle point.
Second-order condition: an example
For f(x, y) = x^2 + 3y^2 the Hessian is diag(2, 6), both positive, so the stationary point at the origin is a minimum.
Related terms
More Calculus optimisation terms
- Sharpness-aware minimisation
- Simulated annealing
- Stationary point
- Step decay
- Stochastic gradient descent
- Strong convexity
- Subgradient
- Subgradient method
Where you learn it
Second-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.