proj_l1¶

odl.solvers.nonsmooth.proximal_operators.proj_l1(x, radius=1, out=None)[source]¶

Projection onto l1-ball.

Projection onto:

``{ x \in X | ||x||_1 \leq r}``

with r being the radius.

Parameters:

spaceLinearSpace: Space / domain X.
radiuspositive float, optional: Radius r of the ball.

Returns:

prox_factorycallable: Factory for the proximal operator to be initialized.

See also

proximal_linfty: proximal for l-infinity norm
proj_simplex: projection onto simplex

Notes

The projection onto an l1-ball can be computed by projection onto a simplex, see [D+2008] for details.

References

[D+2008] Duchi, J., Shalev-Shwartz, S., Singer, Y., and Chandra, T. Efficient Projections onto the L1-ball for Learning in High dimensions. ICML 2008, pp. 272-279. http://doi.org/10.1145/1390156.1390191