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123. Projection onto box constraints

easy
GeneralGeneral
senior

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.

Π[l,u](x)i=min⁡(max⁡(xi, li), ui)\Pi_{[l,u]}(x)_i = \min\left(\max(x_i,\, l_i),\, u_i\right)

Requirements

Implement the function

python

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

Output:

python
Input Signature
ArgumentType
xnp.ndarray
lowernp.ndarray
uppernp.ndarray
Output Signature
Return NameType
valuenp.ndarray

Constraints

  • Use NumPy; no SciPy or helpers.

  • Return NumPy array.

  • Do not mutate inputs in-place.

Hint 1

Use np.clip(x, lower, upper) for a direct vectorized solution.

Hint 2

Alternatively, np.minimum(np.maximum(x, lower), upper) achieves the same result.

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GeneralGeneral
Levels
senior
entry
Tags
numpy
projection
clipping
constrained-optimization
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