## 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()
```


```python

```

91c2bd9fd79054cad36dff668ceca6a0e581698a
ipynb
Jupyter Notebook
doc/source/problems/single/rosenbrock.ipynb
gabicavalcante/pymoo
1711ce3a96e5ef622d0116d6c7ea4d26cbe2c846
Apache-2.0
2018-05-22T17:38:02.000Z
2022-02-28T03:34:33.000Z
doc/source/problems/single/rosenbrock.ipynb
gabicavalcante/pymoo
1711ce3a96e5ef622d0116d6c7ea4d26cbe2c846
Apache-2.0
2022-01-03T19:36:36.000Z
2022-03-30T03:57:58.000Z
doc/source/problems/single/rosenbrock.ipynb
gabicavalcante/pymoo
1711ce3a96e5ef622d0116d6c7ea4d26cbe2c846
Apache-2.0
2021-11-22T08:01:47.000Z
2022-03-11T08:53:58.000Z
Qwen/Qwen-72B
1. YES
2. YES