A Tutorial when starting with a new manifold

[kellertuer]

This is an approach to resolve #305.

Maybe it is also a good idea on this PR to first have a few more “Technical Details” pages per solver similar to https://manoptjl.org/stable/solvers/gradient_descent.html#Technical-Details.

• [x] finished a new tutorial
• [x] introduce vale.sh to reduce errors and formatting in docs – though for now just in md files not yet in doc strings.
• add “Technical Details” sections to other solvers
  • [x] ARC solver
  • [x] alternating gradient descent
  • [x] ALM
  • [x] Chambolle–Pock
  • [x] CG
  • [x] DoC
  • [x] DouglasRachford
  • [x] EPM
  • [x] gradient descent
  • [x] Levenbeg–Marquardt
  • [x] Nelder–Mead
  • [x] particle swarm
  • [x] primal dual semi smooth Newton
  • [x] quasi Newton
  • [x] SGD
  • [x] tCG
  • [x] trust regions

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Codecov Report

All modified and coverable lines are covered by tests :white_check_mark:

Comparison is base (c1fc4a5) 99.74% compared to head (77d8768) 99.74%.

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```diff @@ Coverage Diff @@ ## master #314 +/- ## ======================================= Coverage 99.74% 99.74% ======================================= Files 79 79 Lines 7353 7353 ======================================= Hits 7334 7334 Misses 19 19 ```

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[kellertuer]

@blegat before continuing with more technical details sections (they take a bit of time not to miss a function) – can you check whether a tutorial like https://manoptjl.org/previews/PR314/tutorials/ImplementOwnManifold.html is what you would have liked to have?

[blegat]

Yes, it's exactly what I had in mind!

[kellertuer]

Great! Then I will carefully add the technical details sections for the other solvers as well; probably also for step sizes and debugs.

[kellertuer]

While a few might still be challenging (Chambolle-Pock), I think most (CG, SGD, EPM,...) will just be copies of gradient descent in the technical details. Still good to check them.

And since I am redoing the docs a bit anyways, I will also try to minimise Vale warnings along the way (we at least do not have Vale errors any longer by now).

[kellertuer]

I now added a technical section to all solvers that lists (and currently also explains a bit) which functions are required what for. One could maybe shorten that to just listing functions.

Besides that I will maybe wait a day or two whether vale will get Julia code/docstring support and reiterate here again then. If they are not that fast I might just merge this for now.