pyproximal.L1Ball

class pyproximal.L1Ball(n: int, radius: float, maxiter: int = 100, xtol: float = 1e-05)

L1 ball proximal operator.

Proximal operator of the \(\ell_1\) ball: \(L1_{r} = \{ \mathbf{x}: \|\mathbf{x}\|_1 \leq r \}\).

Parameters:

nint

Number of elements of input vector

radiusfloat

Radius

maxiterint, optional

Maximum number of iterations used by scipy.optimize.bisect

xtolfloat, optional

Absolute tolerance of scipy.optimize.bisect

Notes

As the L1 ball is an indicator function, the proximal operator corresponds to its orthogonal projection (see pyproximal.projection.L1BallProj for details.

Methods

__init__(n, radius[, maxiter, xtol])
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)