Use augmented Lagrangian for minimal covers

[timholy]

Replace penalty continuation with a multiplier iteration that keeps penalty weights moderate and improves KKT accuracy.

• adapt κ when residual contraction slows
• cache dense and CHOLMOD factorizations by κ and active set
• replace κs with κ and maxouter, and report KKT progress

Assisted-by: Claude Fable 5 (claude-fable-5) noreply@anthropic.com

[codecov]

Codecov Report

❌ Patch coverage is 99.20635% with 2 lines in your changes missing coverage. Please review.
✅ Project coverage is 98.91%. Comparing base (c127c5f) to head (31f0d1a).

Files with missing lines	Patch %	Lines
src/minimal_covers.jl	99.20%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #52      +/-   ##
==========================================
- Coverage   98.92%   98.91%   -0.02%     
==========================================
  Files          15       15              
  Lines        3643     3785     +142     
==========================================
+ Hits         3604     3744     +140     
- Misses         39       41       +2     

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