Correct xi in SolverCore.solve! in LM and R2N solvers

[MohamedLaghdafHABIBOULLAH]

No description provided.

[Copilot]

Pull Request Overview

This PR corrects the model function mk in the SolverCore.solve! method for both LM and R2N solvers by adding a quadratic regularization term.

• Adds the regularization term - 1/2 * σk * dot(d, d) to the model function mk
• Ensures consistent mathematical formulation across both solver implementations

Reviewed Changes

Copilot reviewed 2 out of 3 changed files in this pull request and generated no comments.

File	Description
src/R2N.jl	Updates model function to include quadratic regularization term
src/LM_alg.jl	Updates model function to include quadratic regularization term

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 84.41%. Comparing base (e0f214d) to head (7b4748c).
⚠️ Report is 247 commits behind head on master.

Additional details and impacted files

@@             Coverage Diff             @@
##           master     #239       +/-   ##
===========================================
+ Coverage   61.53%   84.41%   +22.88%     
===========================================
  Files          11       13        +2     
  Lines        1292     1630      +338     
===========================================
+ Hits          795     1376      +581     
+ Misses        497      254      -243     

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[MohamedLaghdafHABIBOULLAH]

Should we merge? @dpo @MaxenceGollier

[Copilot]

Pull Request Overview

Copilot reviewed 2 out of 3 changed files in this pull request and generated 2 comments.

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[MaxenceGollier]

I think dpo had a comment (on zulip)

[MohamedLaghdafHABIBOULLAH]

@dpo is this ok for you?

[MaxenceGollier]

Why should we remove this ?
solver.subpb.model.σwill not be updated anywhere ?

[dpo]

I think that line needs to stay. It's the computation of $\xi_k$ that is inefficient. Please grab the model value from the stats and subtract the $\tfrac{1}{2} \sigma |s|^2$ to avoid recomputing it.

[MohamedLaghdafHABIBOULLAH]

We should close this as this issue has been treated here PR by Maxence.