[codex] Refine MindtPy no-discrete short-circuit routing

[bernalde]

Summary

• reuse structure already classified during MindtPy utility-block setup instead of re-walking constraint polynomial degree in the no-discrete short-circuit path
• classify continuous short-circuit models as LP, QP, QCP, or NLP and route QP/QCP cases to the configured mip_solver only when that solver interface explicitly supports the required quadratic structure
• preserve the current no-fallback-on-failure behavior and mirror direct-solve results against the objective on the original model

Root cause

The no-discrete short-circuit path was doing two things that made future routing work harder:

• it duplicated structural analysis that had already happened during utility-block setup
• it treated every continuous non-LP model as an NLP, so continuous QP/QCP models never used the configured MIP solver even when that solver could handle them directly

Impact

This keeps the short-circuit path scoped and predictable while enabling capability-aware routing for continuous quadratic models. Unsupported quadratic cases still go through the NLP solver, and MIP failures are not silently retried with NLP.

Validation

• Black formatting verified in the active conda base environment for the touched files
• conda run -n base python -m pytest pyomo/contrib/mindtpy/tests/test_mindtpy_no_discrete.py -q

[bernalde]

Overall the classification and routing logic is sound and the new tests are well-structured. The main concern is a subtle overlap in the new constraint lists that, while currently harmless, will mislead readers and could easily cause counting bugs. A few smaller items follow.

All 22 tests pass (including the 6 integration tests against ipopt + appsi_highs). The broader MindtPy suite (78 tests) also passes without regressions.

[bernalde]

I addressed the actionable review items in a014410. The main behavioral change is that the direct-solve structure cache now uses boolean structural flags instead of overlapping lists, which keeps short-circuit classification independent of quadratic_strategy without ambiguous list membership. I also removed the eager objective-degree lookup, hoisted the duplicated problem-type label map, added the HiGHS TODO note, renamed the generic test fake, and added regression coverage for LP routing, the QCP plus unsupported quadratic-objective branch, and the quadratic_strategy == 2 structural case. Validation on this branch was conda run -n base python -m pytest pyomo/contrib/mindtpy/tests/test_mindtpy_no_discrete.py -q, which now passes with 25 tests.

[bernalde]

All six items from the first review are addressed. Tests grew from 22 to 25 and all pass, including the integration tests against ipopt + appsi_highs. The broader MindtPy suite (81 tests) also passes without regressions.

The switch from full lists to boolean flags for quadratic/nonquadratic classification is a clean simplification that eliminates the overlap concern entirely. The new test_short_circuit_qcp_detection_ignores_quadratic_strategy test is a good addition that directly validates the interaction between quadratic_strategy=2 and the short-circuit routing.

One minor remaining nit below, otherwise this looks good to go.

[bernalde]

I did a full pass over this PR and one additional cleanup stood out before it goes upstream: the docstrings around the no-discrete short-circuit path in pyomo/contrib/mindtpy/algorithm_base_class.py still described only LP/NLP behavior, even though this branch now classifies and routes continuous models as LP/QP/QCP/NLP and may use either the configured MIP solver or the NLP solver. That cleanup is now addressed in da366fb, which updates the model_is_valid() and _mirror_direct_solve_results() docstrings to match the implemented behavior.

[bernalde]

The classification and routing logic is sound, the switch from parallel constraint lists to boolean flags is cleaner, and the test suite is well-structured. The items below are what I found after a pass through the final state of the branch.