proximal_convex_conj_linfty

odl.solvers.nonsmooth.proximal_operators.proximal_convex_conj_linfty(space)[source]

Proximal operator factory of the Linfty norm/distance convex conjugate.

Implements the proximal operator of the convex conjugate of the functional

F(x) = \|x\|_\infty

with x in space.

Parameters
spaceLinearSpace or ProductSpace of LinearSpace spaces

Domain of the functional F

Returns
prox_factoryfunction

Factory for the proximal operator to be initialized.

See also

proj_l1

orthogonal projection onto balls in the 1-norm

Notes

The convex conjugate F^* of the functional

F(x) = \|x\|_\infty.

is in the case of scalar-valued functions given by the indicator function of the unit 1-norm ball

F^*(y) = \iota_{B_1} \big( y \big).