Introduction of R2NLS Solver in JSOSolvers

[farhadrclass]

This PR introduces the new R2NLS solver, An inexact second-order quadratic regularization method designed specifically for nonlinear least-squares problems.

The objective is to solve min ½‖F(x)‖² where F: ℝⁿ → ℝᵐ is a vector-valued function defining the least-squares residuals.

[codecov[bot]]

Codecov Report

Attention: Patch coverage is 71.93676% with 71 lines in your changes missing coverage. Please review.

Project coverage is 85.96%. Comparing base (52caf59) to head (77719c5). Report is 13 commits behind head on main.

Files with missing lines	Patch %	Lines
src/utilities.jl	0.00%	51 Missing :warning:
src/R2NLS.jl	90.09%	20 Missing :warning:

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #303      +/-   ##
==========================================
- Coverage   89.00%   85.96%   -3.04%     
==========================================
  Files           7        9       +2     
  Lines        1200     1453     +253     
==========================================
+ Hits         1068     1249     +181     
- Misses        132      204      +72     

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[farhadrclass]

@tmigot Thanks for the review,

I see your point on QRMumps but, one of the main focus of this PR and my code is to use the QRMumps and hence I put them here (I was thinking to move them to a different location after but for now I think it is required for this PR), What do you think?

On the tests reviews, I agree, I will clean it up and update it asap and also the same with documents

Thanks for the review

[tmigot]

@tmigot Thanks for the review,

I see your point on QRMumps but, one of the main focus of this PR and my code is to use the QRMumps and hence I put them here (I was thinking to move them to a different location after but for now I think it is required for this PR), What do you think?

On the tests reviews, I agree, I will clean it up and update it asap and also the same with documents

Thanks for the review

I don't really understand why. I get that the point of your code is to use the QRMumps, but we push all the code in several PR because we also need to make sure that it's correct and the best (and fastest) way to do it is by having focused PR. The idea is to have a first PR focus on the algorithm, and then another one is QRMumps.