### Sphere

##### Mathematical Definition
###### Latex
f(x) = {\sum_{i=1}^{n} x_i^{2}}
##### Description and Features

Dimensions: d

The Sphere function has d local minima except for the global one. It is continuous, convex and unimodal. The plot shows its two-dimensional form.

• The function is continuous.
• The function is convex.
• The function can be defined on n-dimensional space.
• The function is differentiable.
• The function is separable.
• The function is unimodal.
##### Input Domain

The function can be defined on any input domain but it is usually evaluated on $x_i \in [-5.12, 5.12]$ for $i = 1, …, d$ .

##### Global Minima

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

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

def function(x):
x = np.array(x)
return np.sum(np.square(x))