[petsc-dev] quasi-newton approximations

[Oxberry, Geoffrey Malcolm]

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<mailto:petsc-dev-bounces at mcs.anl.gov>> on behalf of Matthew Knepley <knepley at gmail.com<mailto:knepley at gmail.com>>
Date: Tuesday, August 30, 2016 at 2:02 PM
To: "Munson, Todd" <tmunson at mcs.anl.gov<mailto:tmunson at mcs.anl.gov>>
Cc: petsc-dev <petsc-dev at mcs.anl.gov<mailto: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<mailto: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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