# Brent 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 $x_i \in [-20, 0]$ for $i=1, 2$.

# Global Minima

The function has one global minimum at $f(\textbf{x}^{\ast})= e^{-200}$ located at $\mathbf{x^\ast}=(-10, -10)$.

# Implementation

An implementation of the **Brent 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