pyproximal.projection.SimplexProj

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

Simplex projection.

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

Given a Simplex set defined as:

\[\Delta_n(r) = \{ \mathbf{x}: \sum_i x_i = r,\; x_i \geq 0 \}\]

its orthogonal projection is simply given by projection of the intersection between a hyperplane and a box with chosen radius and bounds equal to 0 and inf (see pyproximal.projection.HyperPlaneBoxProj for more details).

Methods

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