pyproximal.EuclideanBall

class pyproximal.EuclideanBall(center: ndarray[tuple[Any, ...], dtype[_ScalarT]] | float, radius: float)

Euclidean ball proximal operator.

Proximal operator of the Euclidean ball: \(Eucl_{[c, r]} = \{ \mathbf{x}: ||\mathbf{x} - \mathbf{c}||_2 \leq r \}\).

Parameters:

centernumpy.ndarray or float

Center of the ball

radiusfloat

Radius

Notes

As the Euclidean ball is an indicator function, the proximal operator corresponds to its orthogonal projection (see pyproximal.projection.EuclideanBallProj for details.

Methods

__init__(center, radius)
affine_addition(v)	Affine addition
chain(g)	Chain
grad(x)	Gradient of the Moreau envelope of the function.
postcomposition(sigma)	Postcomposition
precomposition(a, b)	Precomposition
prox(**kwargs)
proxdual(**kwargs)

Examples using pyproximal.EuclideanBall

Dykstra’s algorithms

Dykstra's algorithms

Basis Pursuit

Basis Pursuit