For preconditioners, I use them as a default for unconstrained and bound constrained problems. They can be overridden by someone who knows a good preconditioner for their particular problem.
For more general constrained problems, its harder. But they could be part of your saddle point problem preconditioner. Note: we already use QN methods in TAO for the some reduced space methods where we use a QN approximation to the reduced Hessian matrix, primarily because we never want to actually form the reduced Hessian matrix. It could still be used as a preconditioner in a flexible CG method using the product form of the reduced Hessian. Todd. > On Aug 30, 2016, at 4:13 PM, Oxberry, Geoffrey Malcolm <[email protected]> > wrote: > > I think refactoring to enable use of QN approximations in more methods is a > good idea. As I’m sure you both are aware, some IPMs and SQP methods admit QN > approximations, and it would be good to have this option on the command line > for more methods (e.g., TAOIPM, the nascent SQP implementation), especially > where attempting to form even the action of the Hessian is onerous. > > For the optimization methods, it’s not immediately clear that extracting them > as a PC makes sense to me. I’d have to think about it more. In many > algorithms (e.g., in IPOPT), using the QN approximation also enables more > efficient linear algebra via Sherman-Morrison-Woodbury, but it’s not clear to > me that this modification is really appropriate for some of the possible > algorithm combinations in TAO. It makes sense for TAOIPM with KSPPREONLY and > PCLU with SuperLU or another package capable of pivoting with zeroes on the > diagonal, but if an actual Krylov subspace method is used, I’m not sure it > makes sense anymore. > > Geoff > > From: <[email protected]> on behalf of Matthew Knepley > <[email protected]> > Date: Tuesday, August 30, 2016 at 2:02 PM > To: "Munson, Todd" <[email protected]> > Cc: petsc-dev <[email protected]> > Subject: Re: [petsc-dev] quasi-newton approximations > > I think we should extract them the same way as SNESMFFD. Using them as a PC > is a good idea. > > Matt > > On Tue, Aug 30, 2016 at 1:18 PM, Munson, Todd <[email protected]> wrote: > > One of the common concepts for TAO and SNES is the quasi-Newton > approximations. > SNES seems to only use them in SNESQN (for non-symmetric matrices) and TAO > uses > them in TAOLMVM and TAOBLMVM (for symmetric matrices). TOA also allows them > to > be used as a preconditioner for the Hessian-based line-search and trust-region > methods. > > Should we consider extracting some common class for these approximations and > the associated operations or just leave them as separate things? > > Todd. > > > > > -- > What most experimenters take for granted before they begin their experiments > is infinitely more interesting than any results to which their experiments > lead. > -- Norbert Wiener
