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