[petsc-dev] Semismooth Newton

[Todd Munson]

> How does one precondition a system like that?  Presumably, the user may at
> best be able to provide a preconditioner for JF.
> 
> If JF responds well to multigrid, then it may be possible to use AMG-KKT
> to coarsen the constraint Hessian, but how does MG perform for the sum
> JF + Hc?  There is also the problem of smoothing, although, if JF and Jc
> are sparse, then DD may be an option with a direct solve on subdomains.
> 
> Anything more definitive on preconditioning these systems?

If the constraints are linear, then there are no modifications to JF, so
your preconditioner for JF should be fine.  Then you either construct a
preconditioner for the KKT system or you use something like what the
Sandian's use for their optimization methods.

For nonlinear; not a clue.  If the symmetric part can be approximated well
by a low-rank matrix, then you might combine the preconditioner for JF 
with a quasi-newton approximation to Hc?

Cheers, Todd.