Class AugmentedProximalOperator

source code

      object --+    
               |    
ProximalOperator --+
                   |
                  AugmentedProximalOperator

Known Subclasses:

• combinedfunctions.AugmentedLinearRegressionL1L2TV

Given the problem

    min. f(x)
    s.t. x = z

the augmented Lagrangian is

    L(x)  = f(x) + y'(x - z) + (rho / 2) * ||x - z||²
        === f(x) + (rho / 2) * ||x - z + u||²
          = prox_{(1 / rho) * f}(z - u)

where y = rho * u is a dual variable associated to the constraint x = z,
and ||.||² is the squared L2 norm. We note that this is the proximal
operator of f(x) at the point z - u.

This Function represents the proximal operator of f at z - u, given the
augmented Lagrangian.

Parameters
----------
rho : Non-negative float. The regularisation constant for the augmented
        Lagrangian.