pyproximal.projection.L0BallProj#

class pyproximal.projection.L0BallProj(radius)[source]#

\(L_0\) ball projection.

Parameters
radiusint

Radius

Notes

Given an L0 ball defined as:

\[L0_{r} = \{ \mathbf{x}: ||\mathbf{x}||_0 \leq r \}\]

its orthogonal projection is computed by finding the \(r\) highest largest entries of \(\mathbf{x}\) (in absolute value), keeping those and zero-ing all the other entries. Note that this is the proximal operator of the corresponding indicator function \(\mathcal{I}_{L0_{r}}\).

Methods

__init__(radius)