# Rastrigin Function

# Mathematical Definition

# Plots

The contour of the function is as presented below:

# Description and Features

- The function is continuous.
- The function is convex.
- The function is defined on n-dimensional space.
- The function is multimodal.
- The function is differentiable.
- The function is separable.
- The function is .

# 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 $i = 1, …, n$ .

# Global Minima

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

# Implementation

An implementation of the **Rastrigin Function** with MATLAB is provided below.

The function can be represented in Latex as follows: