Adding regularization objective option to parmest

[sscini]

Fixes # .

Summary/Motivation:

Currently, the only default objective is the standard SSE objective. This edit provides the capability to add a
regularization term to the SSE objective with a prior FIM and reference parameter values.

Changes proposed in this PR:

• Added prior_FIM and theta_ref as keyword arguments for Estimator
• Added options within Estimator to apply the regularization term to SSE if the new arguments were defined

TODO before converting from draft

• Receive feedback from collaborators on logical setup
• Finish edits and debug
• Confirm functionality with examples

Legal Acknowledgement

By contributing to this software project, I have read the contribution guide and agree to the following terms and conditions for my contribution:

1. I agree my contributions are submitted under the BSD license.
2. I represent I am authorized to make the contributions and grant the license. If my employer has rights to intellectual property that includes these contributions, I represent that I have received permission to make contributions and grant the required license on behalf of that employer.

[sscini]

@djlaky @adowling2 Please provide early feedback

[adowling2]

@sscini See my early feedback.

[sscini]

UPDATE (07/15/25); Intended to be added AFTER Shammah's weighted SSE PR (#3535) and follow a similar format, adding another option for available objectives using Enums.

Currently preparing for next stage of review

[sscini]

@adowling2 @djlaky Made some edits to this finally. Meant to follow Shammah's layout in PR #3535, waiting to merge, currently some conflicts I cannot resolve on my end.

Made it's own full objective instead of a term to add. Also added weighting term.

Ready for next round of review.

[sscini]

Will not be actively worked on before finalization of _Q_opt_blocks. Closing for now to resume in the future.

[sscini]

@blnicho Thank you for fixing the formatting issue. I tried to resolve the merge conflict after _Q_opt and was not near my laptop. Both of the failing tests are not related to my tests.

[blnicho]

@sscini I have a few minor comments and questions but otherwise this looks fine.

[sscini]

@blnicho @mrmundt Thank you both for all your comments. Running new checks now, but I believe all are addressed.

[codecov]

Codecov Report

❌ Patch coverage is 81.32530% with 31 lines in your changes missing coverage. Please review.
✅ Project coverage is 90.11%. Comparing base (787c6ff) to head (ac505bb).
⚠️ Report is 73 commits behind head on main.

Files with missing lines	Patch %	Lines
pyomo/contrib/parmest/parmest.py	80.88%	26 Missing ⚠️
.../examples/rooney_biegler/regularization_example.py	83.33%	5 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #3550      +/-   ##
==========================================
- Coverage   90.12%   90.11%   -0.01%     
==========================================
  Files         905      906       +1     
  Lines      107490   107638     +148     
==========================================
+ Hits        96873    97000     +127     
- Misses      10617    10638      +21     

Flag	Coverage Δ
builders	29.10% <5.42%> (-0.02%)	⬇️
default	86.46% <81.32%> (?)
expensive	35.18% <21.68%> (?)
linux	87.61% <81.32%> (-2.02%)	⬇️
linux_other	87.61% <81.32%> (-0.01%)	⬇️
oldsolvers	28.05% <5.42%> (-0.04%)	⬇️
osx	82.99% <81.32%> (+<0.01%)	⬆️
win	85.53% <81.32%> (+<0.01%)	⬆️

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[slilonfe5]

@sscini @blnicho I’ve noticed that the code coverage of ParmEst is now at 81%, down from 90%. Is this something to fix in this PR while we’re at it? So someone in the future doesn’t have to worry about this.

[sscini]

@sscini @blnicho I’ve noticed that the code coverage of ParmEst is now at 81%, down from 90%. Is this something to fix in this PR while we’re at it? So someone in the future doesn’t have to worry about this.

Great point @slilonfe5. I am planning to add a few today. Also, is ParmEst at 81% or my change lines in this code? I think what it says here is my changes are at 81% but I could be wrong.