# Schwefel Function

# Mathematical Definition

# Plots

The contour of the function:

# Description and Features

- The function is continuous.
- The function is not convex.
- The function can be defined on n-dimensional space.
- The function is multimodal.
- The function is not .

# Input Domain

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

# Global Minima

$f(\textbf{x}^{\ast}) = 0$ at $\textbf{x}^{\ast} = (420.9687, …, 420.9687)$

# Implementation

An implementation of the **Schwefel Function** with MATLAB is provided below. **Schwefel Function** can be implemented with a `for`

loop that iterates over all the components of the input vector but, MATLAB and Octave have built-in facilities that makes the implementation more efficient and concise.

The function can be represented in Latex as follows:

# References:

- http://www.sfu.ca/~ssurjano