petsc's QN routines uses limited-memory variable metric format, which means 
explicit hessian is not constructed.
Instead of creating explicit hessian, TAO uses MatSolve, and MatMult, to 
"access" the hessian. So you can have access to Hx, and H^{-1}x, but not H 
matrix by itself.
And as of right now, there isn't a way to access such Hx, and H^{-1}x. (which 
also means that even if the routines to access Hx, H^{-1}x were there, getting 
those at each iteration doesn't really show much information, I think.)


(Sorry for email reply-chain screw up..)

From: Stefano Carli <[email protected]>
Subject: [petsc-users] obtaining estimated Hessian in BQNLS
Date: April 25, 2023 at 4:15:35 AM EDT
To: "[email protected]" <[email protected]>
Message-Id: <[email protected]>

Dear PETSc developers,

I’m using PETSc version 3.14.1 coupled to a Fortran code, and I was wondering 
if there is a way of obtaining in output, possibly at each iteration, the 
estimated Hessian matrix for the BQNLS method.

Thank you in advance and best regards,
Stefano Carli

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