# Ackley N. 2 Function

# Mathematical Definition

# Plots

A contour of the function is presented below:

# Description and Features

- The function is convex.
- The function is defined on 2-dimensional space.
- The function is non-separable.
- The function is differentiable.

# Input Domain

The function can be defined on any input domain but it is usually evaluated on $x_i \in [-32, 32]$ for $i=1, 2$.

# Global Minima

The function has a global minimum at $f(\textbf{x}^{\ast})=-200$ located at $\mathbf{x^\ast}=(0, 0)$.

# Implementation

An implementation of the **Ackley N. 2 Function** with `MATLAB`

is provided below.

The function can be represented in Latex as follows:

# See Also:

# References:

- Momin Jamil and Xin-She Yang, A literature survey of benchmark functions for global optimization problems, Int. Journal of Mathematical Modelling and Numerical Optimisation}, Vol. 4, No. 2, pp. 150–194 (2013), arXiv:1308.4008
- D. H. Ackley, “A Connectionist Machine for Genetic Hill-Climbing,” Kluwer, 1987.