# Rosenbrock Function

# Mathematical Definition

In this formula, the parameters $a$ and $b$ are constants and are generally set to $a=1$ and $b=100$.

# Plots

The contour of the function is as presented below:

# Description and Features

- The function is continuous.
- The function is convex.
- The function is defined on n-dimensional space.
- The function is multimodal.
- The function is differentiable.
- The function is non-separable.

# Input Domain

The function can be defined on any input domain but it is usually evaluated on $x_i \in [-5, 10]$ for $i=1, …, n$ .

# Global Minima

The function has one global minimum $f(\textbf{x}^{\ast})=0$ at $\textbf{x}^{\ast} = (1, …, 1)$.

# Implementation

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

The function can be represented in Latex as follows:

# References:

- http://www.sfu.ca/~ssurjano/rosen.html
- https://en.wikipedia.org/wiki/Test_functions_for_optimization
- 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