[lachlangrose]

Draft, stacked on #377 (the ADMM scaling fix), which is stacked on #374. Its diff against master includes those commits until they merge; the change here is the last commit.

admm_solve returned after nmajor iterations without saying whether it had converged. #377 found that with the default admm_weight=0.01 the sparse dome test is still unconverged after 200 iterations (primal residual 0.056 against a tolerance of 0.0025, 4 of 24 bounds violated) and the solver gave no sign of it.

Change

The major loop now records how it ended. If it used every iteration without meeting both the primal and dual tolerances it logs a warning:

ADMM used all 200 iterations without converging: primal residual 0.056 (tolerance 0.0025), dual residual ... (tolerance ...). The inequality constraints may still be violated. Try a larger admm_weight (the final value used was 0.01) or a larger nmajor.

• Not reported: a solve that converged, and a solve that stopped because the model stopped changing (model_update_tol, which the caller asks for).
• Nothing else changes: same return value, same solution, the default penalty is untouched. It is a log warning only; the ok flag returned by solve_system is still True. I chose not to change that flag because other code treats it as "the solve ran".

Tests (added to test_inequality_enforcement.py)

• Sparse dome scenario: the default penalty warns once, naming the iteration count, both residuals with tolerances and admm_weight; admm_weight=1.0 converges, does not warn, and enforces the bounds.
• A small exact problem (data pull two bounded unknowns above their bounds): converged in time, no warning; admm_weight=1e-4, nmajor=20 warns and the bounds really are violated, so the warning is true; model_update_tol stop, no warning; nmajor=3 (fewer than min_iterations=5, so it cannot be declared converged) warns.
• With the source change reverted exactly the three tests that expect a warning fail.
• packages/loop_interpolation/tests: 618 passed, 46 skipped, 4 xfailed (includes the golden tests). ruff: no new findings.

Notes

• The default-penalty xfail from test: pin the recipe and inequality-constraint problems (strict xfail) #374/fix: scale the inequality rows with the equality system in the ADMM solve #377 stays: the penalty is still too weak there, it just now warns. Its reason string is updated.
• A problem with no inequality rows does not reach this code: ADMM(0) raises nelements must be greater than 0 first (the error I saw in the earlier investigation). I did not change that.
• The cg solver silently dropping inequality data is a different path and is not addressed here (still an xfail).

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