Added precompilation for nonnegative least squares

[aris-mav]

Please refer to discourse post:
https://discourse.julialang.org/t/excessively-long-ttfx-with-optimization-and-optimizationoptimjl/118457/7

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

Add any other context about the problem here.

[ChrisRackauckas]

Note that if you really just need NonlinearLeastSquaresProblem, the things in NonlinearSolve.jl will be faster. We need to document that better.

[aris-mav]

Note that if you really just need NonlinearLeastSquaresProblem, the things in NonlinearSolve.jl will be faster. We need to document that better.

Thanks for the suggestion.
Note that in this case I made a slight mistake in the commit title, although the contents seem alrght.
The keyword should be nonnegative instead of nonliear (although I reckon the constraint would also make it nonlinear in a sense, if I'm not wrong).

[ChrisRackauckas]

Need to update the project toml

[aris-mav]

Need to update the project toml

Just updated it, sorry forgot to do that previously.

[ChrisRackauckas]

Looks good. @Vaibhavdixit02 is that a failure on master?

[Vaibhavdixit02]

@arismavridis could you post the flamegraphs you had put on discourse here as well. Will merge this soon but wanted to get a better understanding of the improvements, also did you run timings for the example you had that triggered this?

[aris-mav]

This is the precompilation for 4x4 matrix:
https://github.com/user-attachments/assets/82b91bf7-f702-4977-8a5d-dfa4d5ef9340

and this is for 35x35 (with 4x4 already precompiled):
https://github.com/user-attachments/assets/09ab6acf-2f94-40c9-aca2-d4add7c1f870

As for timings, do you mean before and after precompilation?
If so, these would be :

@time solve_problem(rand(10,100),rand(10))  #1st run
95.392393 seconds (7.30 M allocations: 638.607 MiB, 0.29% gc time, 99.61% compilation time)

@time solve_problem(rand(10,100),rand(10))  #2nd run
1.916750 seconds (334.38 k allocations: 819.706 MiB, 1.86% gc time).