[petsc-users] Questions on TAO and gradient norm / inner products

[Blauth, Sebastian]

Hello,

 

I have some questions regarding TAO and the use the gradient norm. 

 

First, I want to use a custom inner product for the optimization in TAO (for
computing the gradient norm and, e.g., in the double loop of a quasi-Newton
method). I have seen that there is the method TAOSetGradientNorm
https://petsc.org/release/manualpages/Tao/TaoSetGradientNorm/ which seems to
do this. According to the petsc4py docs
https://petsc.org/release/petsc4py/reference/petsc4py.PETSc.TAO.html#petsc4p
y.PETSc.TAO.setGradientNorm, this should do what I want. However, the method
does not always seem to perform correctly: When I use it with “-tao_type
lmvm”, it really seems to work and gives the correct scaling of the residual
in the default TAO monitor. However, when I use, e.g., “-tao_type bqnls”,
“-tao_type cg”, or “-tao_type bncg”, the (initial) residual is the same as
it is when I do not use the TAOSetGradientNorm. However, there seem to be
some slight internal changes (at least for the bqnls), as the number of
iterations to reach the tolerance changes from 15 without TAOSetGradientNorm
to 17 with TAOSetGradientNorm. 

 

For the context: Here, I am trying to solve a PDE constrained optimal
control problem, which I tackle in a reduced fashion (using a reduced cost
functional which results in an unconstrained optimization using the adjoint
approach). For this, I would like to use the L2 inner product induced by the
FEM discretization, so the L2 mass matrix.

 

Moreover, I noticed that the performance of “-tao_type lmvm” and “-tao_type
bqnls” as well as “-tao_type cg” and “-tao_type bncg” are drastically
different for the same unconstrained problem. I would have expected that the
algorithms are (more or less) identical for that case. Is this to be
expected?

 

Finally, I would like to use TAO for solving PDE constrained shape
optimization problems. To do so, I would need to be able to specify the
inner product used in the solver (see the above part) and this inner product
would need to change in each iteration. Is it possible to do this with TAO?
And could anyone give me some hints how to do so in python with petsc4py?

 

Thanks a lot in advance,

Sebastian

 

 

 

--

Dr. Sebastian Blauth

Fraunhofer-Institut für

Techno- und Wirtschaftsmathematik ITWM

Abteilung Transportvorgänge

Fraunhofer-Platz 1, 67663 Kaiserslautern

Telefon: +49 631 31600-4968

 <mailto:sebastian.blauth at itwm.fraunhofer.de>
sebastian.blauth at itwm.fraunhofer.de

 <https://www.itwm.fraunhofer.de> https://www.itwm.fraunhofer.de

 

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