PyProximal
pyproximal.projection.EuclideanBallProj¶
- class pyproximal.projection.EuclideanBallProj(center: ndarray[tuple[Any, ...], dtype[_ScalarT]] | float, radius: float)[source]¶
Euclidean ball projection.
- Parameters:
- center
numpy.ndarrayorfloat Center of the ball
- radius
float Radius
- center
Notes
Given an Euclidean ball defined as:
\[\operatorname{Eucl}_{[c, r]} = \{ \mathbf{x}: l ||\mathbf{x} - \mathbf{c}||_2 \leq r \}\]its orthogonal projection is:
\[P_{\operatorname{Eucl}_{[c, r]}} (\mathbf{x}) = \mathbf{c} + \frac{r} {max\{ ||\mathbf{x} - \mathbf{c}||_2^2, r\}}(\mathbf{x} - \mathbf{c})\]Note the this is the proximal operator of the corresponding indicator function \(\mathcal{I}_{\operatorname{Eucl}_{[c, r]}}\).
Methods
__init__(center, radius)
