[petsc-dev] quasi-newton approximations

Munson, Todd tmunson at mcs.anl.gov
Tue Aug 30 17:36:34 CDT 2016

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.


> On Aug 30, 2016, at 4:13 PM, Oxberry, Geoffrey Malcolm <oxberry1 at llnl.gov> 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: <petsc-dev-bounces at mcs.anl.gov> on behalf of Matthew Knepley <knepley at gmail.com>
> Date: Tuesday, August 30, 2016 at 2:02 PM
> To: "Munson, Todd" <tmunson at mcs.anl.gov>
> Cc: petsc-dev <petsc-dev at mcs.anl.gov>
> 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 <tmunson at mcs.anl.gov> 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

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