Projecting a vector onto **box constraints** is a common step in constrained optimization and gradient-based methods. In this problem, you’ll implement the projection operator that “clips” each coordinate into a valid interval.

$$
\Pi_{[l,u]}(x)_i = \min\left(\max(x_i,\, l_i),\, u_i\right)
$$

## Requirements

Implement the function
```python
def project_onto_box(x, lower, upper):
    \"""
    Projects a vector onto box constraints (elementwise bounds).

    Args:
        x (np.ndarray): Input vector of length n.
        lower (np.ndarray): Lower bounds of length n.
        upper (np.ndarray): Upper bounds of length n.

    Returns:
        np.ndarray: Projected vector y where each y[i] is in [lower[i], upper[i]].
    \"""
    # Your solution below
```

**Rules:**
- Project each element `x[i]` independently into the interval `[lower[i], upper[i]]`.
- Return a **NumPy array** (don’t modify the input arrays in-place).
- Use only **NumPy** and Python built-in libraries (no SciPy or other helpers).
- Keep it efficient: use vectorized NumPy operations.

## Example

```python
x = np.array([2.5, -1.0, 0.3, 10.0])
lower = np.array([0.0, 0.0, 0.0, 3.0])
upper = np.array([2.0, 5.0, 0.5, 7.0])

project_onto_box(x, lower, upper)
```

Output:
```python
array([2.0, 0.0, 0.3, 7.0])
```

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Projection onto box constraints

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625. Projection onto box constraints

Examples

Constraints

Similar Questions

Argument	Type
x	np.ndarray
lower	np.ndarray
upper	np.ndarray