pyproximal.HalfSpace

class pyproximal.HalfSpace(w: ndarray[tuple[Any, ...], dtype[_ScalarT]], b: float)

Half space proximal operator.

Proximal operator of the half space: \(\operatorname{H}_{[w, b]} = \{ \mathbf{x}: \mathbf{w}^T \mathbf{x} \leq b \}\).

Parameters:

wnumpy.ndarray

Coefficients of the half space

bfloat

bias of the half space

Notes

As the half space is an indicator function, the proximal operator corresponds to its orthogonal projection (see pyproximal.projection.HalfSpaceProj for details.

Methods

__init__(w, b)
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)