### Schwefel

##### Mathematical Definition
###### Latex
f(x) = {418.9829d -{\sum_{i=1}^{n} x_i sin(\sqrt{|x_i|})}}
##### Description and Features

Dimensions: d

The Schwefel function is complex, with many local minima. The plot shows the two-dimensional form of the function.

• The function is continuous.
• The function is convex.
• The function is defined on n-dimensional space.
• The function is multimodal.
##### Input Domain

The function can be defined on any input domain but it is usually evaluated on $x_i \in [-500, 500]$ for $i = 1, …, d$ .

##### Global Minima

The function has one global minimum $f(\textbf{x}^{\ast})=0$ at $\textbf{x}^{\ast} = (420.9687, …, 420.9687)$.

##### Implementation
###### Python Code

def function(x):
x = np.array(x)
alpha = 418.9829
return alpha * len(x) - (x * np.sin(np.sqrt(np.abs(x)))).sum()