Fix hda hull and GLOA benchmark paths

[bernalde]

Summary

• Clamp HDA warm-start values to declared Pyomo variable bounds to remove out-of-bounds construction warnings.
• Add a positive unconverted auxiliary and domain-safe nonlinear algebra so HDA can be reformulated with gdp.hull and used by GDPopt GLOA without invalid inactive-disjunct domains.
• Add focused HDA tests covering warning-free model construction and supported Big-M/Hull GDP transformations.

Tests run

• /home/bernalde/.pixi/bin/pixi run pytest tests/test_hda.py -v --tb=short -> 3 passed.
• /home/bernalde/.pixi/bin/pixi run pytest tests/test_module_imports.py -v --tb=short -> 68 passed.
• /home/bernalde/.pixi/bin/pixi run test -> 287 passed, 1 skipped.
• /home/bernalde/.pixi/bin/pixi run lint -> passed.
• git diff --check -> passed.
• /home/bernalde/.pixi/bin/pixi run gdplib-benchmark warnings --instances hda --strategies gdp.bigm gdp.hull --mode transform --run-id issue67_hda_transform_warnings_final -> 0 warning events, 0 errors.
• /home/bernalde/.pixi/bin/pixi run gdplib-benchmark run --instances hda --strategies gdpopt.gloa --timelimit 60 --solver-profile gams-local --run-id issue67_hda_gloa_60s_unconverted -> result JSON reports GDPopt GLOA optimal with objective 1105.3441871686007; the CLI exited 1 after writing results because of an unrelated post-run summary import error: ModuleNotFoundError: No module named 'generate_benchmark_summary_all'.

Notes

• I did not run a full long solver benchmark matrix or claim a direct Hull MINLP optimum. The default tests stay solver-free, and optional solver-backed benchmarking is kept separate from CI.
• Issue Plan PyPI release workflow and Pixi platform support #104 was considered as a related follow-up, but it concerns release/Pixi policy and is outside this HDA model fix.

Closes #67

[bernalde]

Direct gdp.hull + local DICOPT diagnostic

I dug into the concerning direct gdp.hull result where the gams-local profile reported infeasible with DICOPT.

What I found:

• The original 5 minute direct gdp.hull + local DICOPT run is reproducible as a solver failure/infeasible local MINLP path, not as proof that the HDA GDP model is logically infeasible. The DICOPT log says the relaxed NLP is infeasible and recommends checking the RMINLP.
• The same unfixed direct Hull model is numerically difficult for other solvers too:
  • gdp.hull + GAMS/Gurobi, 300s: reported infeasible (gdp.hull_gams_gurobi.json in run issue67_hda_hull_gurobi_5min_clean).
  • gdp.hull + GAMS/BARON, 300s default options: reported infeasible (gdp.hull_gams_baron.json in run issue67_hda_hull_baron_5min_clean).
• However, the transformed Hull model does contain feasible integer points. Fixing the route found by GDPopt GLOA and then applying/solving Hull with BARON gives:
  • gdp.hull fixed route + BARON, 120s: optimal with lower bound 1105.3399183842237 and upper bound 1105.33991842781.
  • Transforming with Hull first and then fixing the same route also solves with BARON to the same objective range.
• Local continuous solvers are the weak link here:
  • Fixed-route Hull + IPOPTH from the model's default start reports infeasible.
  • Passing warmstart=True through the GAMS interface did not change the fixed-route IPOPTH result.
  • Starting DICOPT from the GLOA route indicators, without fixing them, still reports infeasible.
• A BARON IIS diagnostic did not support true infeasibility. With CompIIS 1, BARON did not return an IIS; it found incumbents and the kept log reported 0 INFEASIBLE. I am treating that run as diagnostic only, not as a replacement benchmark solve.

Conclusion:

The direct gdp.hull + local DICOPT result should be recorded as a local solver/numerical failure for the nonconvex Hull reformulation, not as evidence that the HDA model or the PR's Hull transformation support is wrong. PR #130 fixes construction, transformation, and GDPopt GLOA paths. A robust direct-Hull MINLP solve remains separate follow-up work, likely involving better formulation scaling/initialization and solver-profile-specific handling rather than another narrow deprecation/domain fix in this PR.

[bernalde]

GDPopt LOA nonconvex bound reporting

Another benchmark caveat for this HDA instance: the local gdpopt.loa row reports:

termination: optimal
LB = UB = 1011.6577899409375

That should not be read as a rigorous global certificate. HDA is nonconvex, and LOA's OA/discrete bound is not guaranteed to be valid globally in that setting. Other methods found a better feasible/global solution around 1105.34, so the LOA-reported upper bound of 1011.6577899409375 is not a valid global upper bound for this maximization model.

I opened an upstream Pyomo issue for the result-semantics problem:

Pyomo/pyomo#3947

For this PR, I would record the LOA result as a local/non-rigorous LOA incumbent, not as a certified optimum.