# The Branin test case¶

## Introduction¶

The Branin function is defined in 2 dimensions based on the functions :

and :

Finally, the Branin function is the composition of the two previous functions:

for any .

There are three global minimas:

and :

where the function value is:

We assume that the output of the Branin function is noisy, with a gaussian noise. In other words, the objective function is:

where is a random variable with gaussian distribution.

This time the AEI formulation is used, meaning that the objective has two outputs: the first one is the objective function value and the second one is the noise variance.

Here we assume a constant noise variance:

## References¶

>>> from openturns.usecases import branin_function as branin_function