# Himmelblau Function

# Mathematical Definition

# Plots

The contour of the function:

# Description and Features

- The function is continuous.
- The function is not convex.
- The function is defined on the 2-dimensional space.
- The function is multimodal.

# Input Domain

The function can be defined on any input domain but it is usually evaluated on $x_i \in [-6, 6]$ for $i = 1, 2$.

# Global Minima

The function has four local minima at:

- $f(\textbf{x}^{\ast}) = 0$ at $\textbf{x}^{\ast} = (3, 2)$
- $f(\textbf{x}^{\ast}) = 0$ at $\textbf{x}^{\ast} = (-2.805118, 3.283186)$
- $f(\textbf{x}^{\ast}) = 0$ at $\textbf{x}^{\ast} = (-3.779310, -3.283186)$
- $f(\textbf{x}^{\ast}) = 0$ at $\textbf{x}^{\ast} = (3.584458, -1.848126)$

# Implementation

An implementation of the **Himmelblau Function** with MATLAB is provided below.

The function can be represented in Latex as follows:

# References:

- https://en.wikipedia.org/wiki/Himmelblau%27s_function