proximal_l2¶
- odl.solvers.nonsmooth.proximal_operators.proximal_l2(space, lam=1, g=None)[source]¶
Proximal operator factory of the l2-norm/distance.
Function for the proximal operator of the functional
F
whereF
is the l2-norm (or distance to g, if given):``F(x) = lam ||x - g||_2``
- Parameters:
- space
LinearSpace
Domain of F(x). Needs to be a Hilbert space. That is, have an inner product (
LinearSpace.inner
).- lampositive float, optional
Scaling factor or regularization parameter.
- g
space
element, optional An element in
space
. Default:space.zero
.
- space
- Returns:
- prox_factorycallable
Factory for the proximal operator to be initialized.
See also
proximal_l2_squared
proximal for squared norm/distance
proximal_convex_conj_l2
proximal for convex conjugate
Notes
Most problems are forumlated for the squared norm/distance, in that case use
proximal_l2_squared
instead.The -norm/distance is given by
For a step size , the proximal operator of is given by
where .