# Mathematical Definition

where $m$ and $\beta$ are parameters of the function. The values for these parameters are usually set to $m=5$ and $\beta=15$.

# Plots

A contour of the function is presented below:

# Description and Features

• The function is convex.
• The function is defined on n-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 $x_i \in [-2\pi, 2\pi]$ for $i=1, …, n$.

# Global Minima

The global minimum $f(\textbf{x}^{\ast})=-1$ are located at $\mathbf{x^\ast}=(0, …, 0)$ for $m=5$ and $\beta = 15$.

# Implementation

An implementation of the Xin-She Yang N. 3 Function with MATLAB is provided below.

The function can be represented in Latex as follows:

# 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
• X. S. Yang, “Test Problems in Optimization,” Engineering Optimization: An Introduction with Metaheuristic Applications John Wliey & Sons, 2010. [Available Online]: http://arxiv.org/abs/1008.0549