## 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()
```


```python

```

b65208b62781a0a4ee48e2918a2ca73b0a5dcde5
ipynb
Jupyter Notebook
doc/source/problems/single/zakharov.ipynb
gabicavalcante/pymoo
1711ce3a96e5ef622d0116d6c7ea4d26cbe2c846
Apache-2.0
2018-05-22T17:38:02.000Z
2022-02-28T03:34:33.000Z
doc/source/problems/single/zakharov.ipynb
gabicavalcante/pymoo
1711ce3a96e5ef622d0116d6c7ea4d26cbe2c846
Apache-2.0
2022-01-03T19:36:36.000Z
2022-03-30T03:57:58.000Z
doc/source/problems/single/zakharov.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