# Brown Function

# Mathematical Definition

# Plots

Two contours of the function are 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 $x_i \in [-1, 4]$ for $i=1, …, n$.

# Global Minima

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

# Implementation

An implementation of the **Brown 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