## Zakharov

The Zakharov function has no local minima except the global one. It is shown here in its two-dimensional form.

**Definition**

\begin{align}
\begin{split}
f(x) &=& \sum\limits_{i=1}^n {x_i^2} + \bigg( \frac{1}{2} \sum\limits_{i=1}^n {ix_i} \bigg)^2 + \bigg( \frac{1}{2} \sum\limits_{i=1}^n {ix_i} \bigg)^4, \\[2mm]
&& -10 \leq x_i \leq 10 \quad i=1,\ldots,n
\end{split}
\end{align}

**Optimum**

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

**Contour**


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

problem = get_problem("zakharov", n_var=2)
get_visualization("fitness-landscape", problem, angle=(45, 45), _type="surface").show()
get_visualization("fitness-landscape", problem, _type="contour", contour_levels = 200, colorbar=True).show()
```

a17e810c31495b92361dcd11c275ff2219ab9cda
ipynb
Jupyter Notebook
source/problems/single/zakharov.ipynb
SunTzunami/pymoo-doc
f82d8908fe60792d49a7684c4bfba4a6c1339daf
Apache-2.0
2021-09-11T06:43:49.000Z
2021-11-10T13:36:09.000Z
source/problems/single/zakharov.ipynb
SunTzunami/pymoo-doc
f82d8908fe60792d49a7684c4bfba4a6c1339daf
Apache-2.0
2021-09-21T14:04:47.000Z
2022-03-07T13:46:09.000Z
source/problems/single/zakharov.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