A function in which the region above the graph of the function is a [convex set](/pages/Convex%20set.txt). The prototypical convex function is shaped something like the letter U.[^1]

## Strictly convex function

A strictly convex function has exactly one local minimum point, which is also the global minimum point. The classic U-shaped functions are strictly convex functions. However, some convex functions (for example, straight lines) are not U-shaped.[^1]

## Examples

A lot of the common [loss functions](/pages/Loss%20function.txt), including the following, are convex functions:[^1]

- [L2 loss](/pages/L2%20loss.txt)
- [Log loss](/pages/Log%20loss.txt)
- [L1 regularization](/pages/L1%20regularization.txt)
- [L2 regularization](/pages/L2%20regularization.txt)

## See also

- [Gradient descent](/pages/Gradient%20descent.txt): Many variations of gradient descent are guaranteed to find a point close to the minimum of a strictly convex function.
- [Stochastic gradient descent](/pages/Stochastic%20gradient%20descent.txt): Many variations of stochastic gradient descent have a high probability of finding a point close to the minimum of a strictly convex function.

## Footnotes

[^1]: https://developers.google.com/machine-learning/glossary#convex-function