# Ackley N. 3 Function

# Mathematical Definition

# Plots

Two contours of the function are presented below:

# Description and Features

- The function is not 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 two global minima at $f(\textbf{x}^{\ast})\approx -195.629028238419$ located at $\mathbf{x^\ast}=(\pm0.682584587365898, -0.36075325513719)$.

**Note:** Minima values are obtained with Genetic Algorithm and may not be accurate.

# Implementation

An implementation of the **Ackley N. 3 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.