pyproximal.NuclearBall

class pyproximal.NuclearBall(dims: Tuple[int, ...], radius: float, maxiter: int = 100, xtol: float = 1e-05)

Nuclear ball proximal operator.

Proximal operator of the Nuclear ball: \(N_{r} = \{ \mathbf{X}: \|\mathbf{X}\|_* \leq r \}\).

Parameters

dimstuple

Dimensions of input matrix

radiusfloat

Radius

maxiterint, optional

Maximum number of iterations used by scipy.optimize.bisect

xtolfloat, optional

Absolute tolerance of scipy.optimize.bisect

Notes

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

Methods

__init__(dims, 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)

Examples using pyproximal.NuclearBall

Low-Rank completion via SVD

Low-Rank completion via SVD