combine_proximals¶

odl.solvers.nonsmooth.proximal_operators.combine_proximals(\*factory_list)[source]¶

Combine proximal operators into a diagonal product space operator.

This assumes the functional to be separable across variables in order to make use of the separable sum property of proximal operators.

Parameters

factory_listsequence of callables: Proximal operator factories to be combined.

Returns

diag_opfunction: Returns a diagonal product space operator factory to be initialized with the same step size parameter

Notes

That two functionals $F$ and $G$ are separable across variables means that $F((x, y)) = F(x)$ and $G((x, y)) = G(y)$ , and in this case the proximal operator of the sum is given by

$\mathrm{prox}_{\sigma (F(x) + G(y))}(x, y) = (\mathrm{prox}_{\sigma F}(x), \mathrm{prox}_{\sigma G}(y)).$