FunctionalDefaultConvexConjugate

class odl.solvers.functional.functional.FunctionalDefaultConvexConjugate(*args, **kwargs)

Bases: odl.solvers.functional.functional.Functional

The Functional representing F^*, the convex conjugate of F.

This class does not provide a way to evaluate the functional, it is rather intended to be used for its proximal.

Notes

The proximal is found by using the Moreau identity

which allows the proximal of the convex conjugate to be calculated without explicit knowledge about the convex conjugate itself.

Attributes

adjoint

Adjoint of this operator (abstract).

convex_conj

The original functional.

domain

Set of objects on which this operator can be evaluated.

grad_lipschitz

Lipschitz constant for the gradient of the functional.

gradient

Gradient operator of the functional.

inverse

Return the operator inverse.

is_functional

True if this operator’s range is a Field.

is_linear

True if this operator is linear.

proximal

Proximal factory using the Moreu identity.

range

Set in which the result of an evaluation of this operator lies.

Methods

_call(self, x[, out])	Implementation of the operator evaluation.
bregman(self, point, subgrad)	Return the Bregman distance functional.
derivative(self, point)	Return the derivative operator in the given point.
norm(self[, estimate])	Return the operator norm of this operator.
translated(self, shift)	Return a translation of the functional.

__init__(self, func)

Initialize a new instance.

Parameters

funcFunctional

Functional corresponding to F.