Use preconditioner in Augmented Lagrangian method when CCSA is the sub-method?

[twadleigh]

I'm looking for good solvers for large-scale, sparse, possibly constrained, least squares problems, and CCSA looks to fit the bill just about perfectly, at least for problems without equality constraints.

Of course, using the Augmented Lagrangian method with CCSA would appear to be the path to close the gap. However, my inspection of the implementation of the Augmented Lagrangian method leads me to believe that CCSA's preconditioning feature would not be used in that case.

The preconditioning, though, is an essential feature for making CCSA comparable to other more LS-specific algorithms.

There is an obvious way to compute a semi-definite Hessian approximation of the augmented Lagrangian given a semi-definite approximation of the original objective, so capturing the math shouldn't be hard.

So, a couple of questions:

1. Am I right in believing implementing this would be feasible in this library?
2. Would such a feature be a welcome addition?

If so, I might try to take a stab at a PR.