pyproximal.projection.IntersectionProj

class pyproximal.projection.IntersectionProj(k: int, n: int, sigma: float | ndarray[tuple[Any, ...], dtype[_ScalarT]], niter: int = 100, tol: float = 1e-05)

Intersection of multiple convex sets

Parameters:

kint

Size of vector to be projected

nint

Number of vectors to be projected simultaneously

sigmanumpy.ndarray

Matrix of distances of size \(k \times k\)

niterint, optional

Number of iterations

tolfloat, optional

Tolerance of update

Notes

Given an Intersection of simple sets defined as:

\[K = \bigcap_{1 \leq i_1 < i_2 \leq k} K_{i_1,i_2}, \quad K_{i_1,i_2}= \{ \mathbf{x}: |x_{i_2} - x_{i_1}| \leq \sigma_{i1, i2} \}\]

its orthogonal projection can be obtained using the Dykstra’s algorithm [1].

[1]

A., Chambolle, D., Cremers, and T., Pock, “A Convex Approach to Minimal Partitions”, Journal of Mathematical, 2011.

Methods

__init__(k, n, sigma[, niter, tol])