## Rosenbrock

The definition ca be found in <cite data-cite="rosenbrock"></cite>. It is a non-convex function, introduced by Howard H. Rosenbrock in 1960 and also known as Rosenbrock's valley or Rosenbrock's banana function. 

**Definition**

\begin{align}
\begin{split}
f(x) &=& \sum_{i=1}^{n-1} \bigg[100 (x_{i+1}-x_i^2)^2+(x_i - 1)^2 \bigg] \\
&&-2.048 \leq x_i \leq 2.048 \quad i=1,\ldots,n
\end{split}
\end{align}

**Optimum**

$$f(x^*) = 0 \; \text{at} \; x^* = (1,\ldots,1) $$

**Contour**


```python
import numpy as np
from pymoo.factory import get_problem, get_visualization

problem = get_problem("rosenbrock", n_var=2)
get_visualization("fitness-landscape", problem, angle=(45, 45), _type="surface").show()
```

5eb4814f88f56a5564d62b620579e2f4efada290
ipynb
Jupyter Notebook
source/problems/single/rosenbrock.ipynb
SunTzunami/pymoo-doc
f82d8908fe60792d49a7684c4bfba4a6c1339daf
Apache-2.0
2021-09-11T06:43:49.000Z
2021-11-10T13:36:09.000Z
source/problems/single/rosenbrock.ipynb
SunTzunami/pymoo-doc
f82d8908fe60792d49a7684c4bfba4a6c1339daf
Apache-2.0
2021-09-21T14:04:47.000Z
2022-03-07T13:46:09.000Z
source/problems/single/rosenbrock.ipynb
SunTzunami/pymoo-doc
f82d8908fe60792d49a7684c4bfba4a6c1339daf
Apache-2.0
2021-10-09T02:47:26.000Z
2022-02-10T07:02:37.000Z
Qwen/Qwen-72B
1. YES
2. YES