TR description in optimization tutorial

[peoe]

This PR proposes an addition to the optimization tutorial in order to describe the usage of the trust-region algorithm and parts of the underlying theory.

I'd be glad to get some feedback on the clarity of the wording, especially the distinction of the inner/outer loop mechanic because this is essential for the algorithm.

[github-actions]

Mirroring external branch in external_pr_2181

[TiKeil]

Hi Peter,

thanks for including the TR methods in the tutorial. I think the section is well written and the wording was already quite good. I added some comments that you could commit if you want.
These are mostly just suggestions.

Two major comments:

1. The methods opt_along_path and opt_along_path_adaptively were basically in the tutorial since we did not have the TR method, yet. The TR method can be seen as the certified replacement of the other methods. I think it is a little bit dangerous to sell these two methods before the TR method as they were simply invented for presentational reasons and are rather hacked inside the tutorial, not using any pyMOR algorithm. Thus, I would suggest removing these two methods entirely and only concentrating on the TR method.
2. I know that it is a little bit more work, but I think it would be really great if we could get rid of the 'scipy.optimize.minimize' method entirely.

I do not remember but do we use the same problem as in the TR demo for the tutorial?

Thank you.

[peoe]

Thanks for the extensive review @TiKeil ! For now I have implemented the first part of your recommendations, I'll try and get around to the second part tomorrow.

As far as I can tell, the optimization tutorial uses the problem from the linear_optimization.py demo -- which we simply import in the trust_region.py demo.

[sdrave]

As far as I can tell, the optimization tutorial uses the problem from the linear_optimization.py demo -- which we simply import in the trust_region.py demo.

We now have pymor.models.examples where such models can be placed into. At least if they are interesting enough.

[sdrave]

@peoe, @TiKeil, how should we proceed with this PR? I think this need to come to a conclusion. If need be, I can try to do it, but I'm not sure if I'm the best person for the job.

[TiKeil]

Is there something to decide upon or is it "just" working on finalizing the PR ?

[sdrave]

Is there something to decide upon or is it "just" working on finalizing the PR ?

I think it's just finalizing the tutorial.

[sdrave]

@TiKeil, hard freeze for the next release is in one week. Do you think you find time to take a look at this until then?

[TiKeil]

I'm afraid I will not be able to work on this before the freeze.
But I will look at it asap.

[sdrave]

I'm afraid I will not be able to work on this before the freeze. But I will look at it asap.

Ok, I'll remove the release milestone for now. Release is planned for December 7. As this is only documentation related, it might still get in after hard freeze ..

[sdrave]

@TiKeil, did you have a chance to look at this PR? Soft freeze for the next release would be May 31 ..