Add sigma_cauchy and scp_norm to solver statistics in all solvers

[MohamedLaghdafHABIBOULLAH]

Fix this 252

[Copilot]

Pull Request Overview

This PR adds tracking of sigma_cauchy and scp_norm statistics to solver output across all trust-region and regularization-based solvers in the package. These statistics provide important diagnostic information about the solver's behavior at each iteration.

Key changes:

• Addition of sigma_cauchy (reciprocal of step size parameter) tracking
• Addition of scp_norm (norm of the proximal gradient step) tracking
• Consistent placement of these statistics after they are computed in each solver

Reviewed Changes

Copilot reviewed 7 out of 8 changed files in this pull request and generated 5 comments.

Show a summary per file

File	Description
src/TR_alg.jl	Added sigma_cauchy and scp_norm statistics tracking in the TR solver at initialization and main iteration loop
src/TRDH_alg.jl	Added sigma_cauchy and scp_norm statistics tracking in the TRDH solver for both reduce_TR branches
src/R2_alg.jl	Added scp_norm statistics tracking in the R2 solver at initialization and main iteration loop
src/R2N.jl	Added scp_norm statistics tracking in the R2N solver at initialization and main iteration loop
src/R2DH.jl	Added scp_norm statistics tracking and moved sigma_cauchy to after ν₁ is computed in the R2DH solver
src/LM_alg.jl	Added sigma_cauchy and scp_norm statistics tracking in the Levenberg-Marquardt solver at initialization and main iteration loop
src/LMTR_alg.jl	Added sigma_cauchy and scp_norm statistics tracking in the LMTR solver at initialization and main iteration loop

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[codecov]

Codecov Report

❌ Patch coverage is 84.61538% with 4 lines in your changes missing coverage. Please review.
✅ Project coverage is 84.67%. Comparing base (e0f214d) to head (850248d).
⚠️ Report is 248 commits behind head on master.

Files with missing lines	Patch %	Lines
src/TRDH_alg.jl	33.33%	4 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##           master     #253       +/-   ##
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+ Coverage   61.53%   84.67%   +23.14%     
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  Files          11       13        +2     
  Lines        1292     1651      +359     
===========================================
+ Hits          795     1398      +603     
+ Misses        497      253      -244     

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[dpo]

Would it also be useful to report $\Vert s_k \Vert$ in addition to $\Vert s_{k,cp} \Vert$? PANOC doesn't compute an $s_{k,cp}$, and it could be that $\Vert s_k \Vert < \Vert s_{k,cp} \Vert$.

[MohamedLaghdafHABIBOULLAH]

Would it also be useful to report ‖ s k ‖ in addition to ‖ s k , c p ‖ ? PANOC doesn't compute an s k , c p , and it could be that ‖ s k ‖ < ‖ s k , c p ‖ .

I am not sure if the use of ‖ s k ‖ would be suitable for a stationary measure as in R2N we do not necessarily have ‖ s k ‖ < ‖ s k , c p ‖!

[MaxenceGollier]

Excellent,

I wonder if scp_norm is a good name though. Since we have a sigma_cauchy, wouldn't it be more appropriate to rename scp_norm as step_cauchy_norm or cauchy_point_norm ? Just an idea we might as well just keep scp_norm.