ADMMIteration

class deepinv.optim.optim_iterators.ADMMIteration(**kwargs)

Bases: OptimIterator

Iterator for alternating direction method of multipliers.

Class for a single iteration of the Alternating Direction Method of Multipliers (ADMM) algorithm for minimising :math:` f(x) + lambda g(x)`.

If the attribute g_first is set to False (by default), the iteration is (see this paper):

\[\begin{split}\begin{equation*} \begin{aligned} u_{k+1} &= \operatorname{prox}_{\gamma f}(x_k - z_k) \\ x_{k+1} &= \operatorname{prox}_{\gamma \lambda g}(u_{k+1} + z_k) \\ z_{k+1} &= z_k + \beta (u_{k+1} - x_{k+1}) \end{aligned} \end{equation*}\end{split}\]

where \(\gamma>0\) is a stepsize and \(\beta>0\) is a relaxation parameter.

If the attribute g_first is set to True, the functions \(f\) and \(g\) are inverted in the previous iteration.

forward(X, cur_data_fidelity, cur_prior, cur_params, y, physics, *args, **kwargs)

Single iteration of the ADMM algorithm.

Parameters:

• X (dict) – Dictionary containing the current iterate and the estimated cost.

• cur_data_fidelity (deepinv.optim.DataFidelity) – Instance of the DataFidelity class defining the current data_fidelity.

• cur_prior (deepinv.optim.prior) – Instance of the Prior class defining the current prior.

• cur_params (dict) – Dictionary containing the current parameters of the algorithm.

• y (torch.Tensor) – Input data.

• physics (deepinv.physics) – Instance of the physics modeling the observation.

Returns:

Dictionary {“est”: (x, z), “cost”: F} containing the updated current iterate and the estimated current cost.