pyproximal.projection.L1BallProj#
- class pyproximal.projection.L1BallProj(n, radius, maxiter=100, xtol=1e-05)[source]#
\(L_1\) ball projection.
- Parameters
- n
int Number of elements of input vector
- radius
float Radius
- maxiter
int, optional Maximum number of iterations used by
scipy.optimize.bisect- xtol
float, optional Absolute tolerance of
scipy.optimize.bisect
- n
Notes
Given an L1 ball defined as:
\[L1_{r} = \{ \mathbf{x}: ||\mathbf{x}||_1 \leq r \}\]its orthogonal projection is:
\[P_{L1_{r}} (\mathbf{x}) = sign(\mathbf{x}) P_{\operatorname{Simplex}(r)}(\mathbf{x})\]Note that this is the proximal operator of the corresponding indicator function \(\mathcal{I}_{L1_{r}}\).
Methods
__init__(n, radius[, maxiter, xtol])