# Ackley Function

# Mathematical Definition

In the above equation, the values $a$, $b$ and $c$ are constants and are usually chosen as $a=20$, $b=0.2$ and $c=2\pi$.

# Plots

The contour of the function is as presented below:

# Description and Features

- The function is continuous.
- The function is not 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 $x_i \in [-32, 32]$ for all $i = 1,…,n$.

# Global Minima

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

# Implementation

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

The function can be represented in Latex as follows:

# See also:

# References:

- http://www.sfu.ca/~ssurjano/ackley.html
- https://en.wikipedia.org/wiki/Test_functions_for_optimization
- http://www.cs.unm.edu/~neal.holts/dga/benchmarkFunction/ackley.html, This resource
contains an extensive collection of references for this function. The page also contains an implementation of the function in
`Python`

.