[petsc-users] Questions about TSAdjoint for time dependent parameters

[Zhang, Hong]

On Feb 25, 2020, at 11:21 AM, Sajid Ali <sajidsyed2021 at u.northwestern.edu<mailto:sajidsyed2021 at u.northwestern.edu>> wrote:

Hi Hong,

Thanks for the explanation!

If I have a cost function consisting of an L2 norm of the difference of a TS-solution and some reference along with some constraints (say bounds, L1-sparsity, total variation etc), would I provide a routine for gradient evaluation of only the L2 norm (where TAO would take care of the constraints) or do I also have to take the constraints into account (since I'd also have to differentiate the regularizers) ?

This depends on how you would like to formulate and solve your optimization problem. If you wan to use the built-in regularizers in TAO, then you just need provide gradient evaluation of the L2 norm. But TAO provides interfaces for users to provide customized regularizers and the gradient of them, in this case, again, adjoint can be used for the gradient calculation in the same way you handle objective functions/gradients. Of course, it is also possible to include regularizers in your objective function.

Hong


Thank You,
Sajid Ali | PhD Candidate
Applied Physics
Northwestern University
s-sajid-ali.github.io<http://s-sajid-ali.github.io/>

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