MindtPy short-circuit follow-up: avoid duplicate structure checks and refine continuous QP/QCP routing

[bernalde]

Summary

In the no-discrete short-circuit path, MindtPy currently does two things that are worth revisiting:

1. It recomputes structural information in model_is_valid() by walking polynomial degree over every constraint and the objective, even though the utility block setup has already classified constraints into linear and nonlinear lists.
2. It routes any continuous non-LP model to the NLP solver without considering whether the selected MIP solver can directly handle a continuous QP or QCP.

This issue tracks a follow-up refactor separate from #3861, which should stay focused on returning consistent results and loading primal values in the existing short-circuit path.

Related: #3861

Proposed work

1. Remove duplicate structure checks

Reuse the structure information already built during utility-block setup instead of re-walking polynomial degree in the short-circuit check.

Concretely:

• reuse the preclassified linear/nonlinear constraint lists that are already built for the working model
• cache or reuse the objective degree once where needed
• keep existing quadratic_strategy semantics unchanged unless a separate design decision explicitly changes them

2. Evaluate capability-aware routing for continuous QP/QCP models

Refine the no-discrete short-circuit path so that continuous QP/QCP models can use the selected MIP solver when that solver explicitly supports the required quadratic structure.

Concretely:

• prefer the selected mip_solver for continuous QP models only when its interface explicitly supports quadratic objectives
• prefer the selected mip_solver for continuous QCP models only when its interface explicitly supports quadratic constraints
• otherwise continue routing to the configured nlp_solver
• preserve current behavior for plain LP and general NLP models unless the new routing rules apply

Non-goals

• Do not implement a blanket "try MIP and fall back to NLP on any failure" policy.
• Do not treat infeasible, unbounded, time-limit, or solver-error outcomes from the MIP solver as a signal to silently retry with the NLP solver.
• Do not add a new public config option unless the implementation proves it is necessary.

Test plan

Add targeted short-circuit tests for:

• continuous QP models where a quadratic-capable MIP solver should be preferred
• continuous QCP models only for solver interfaces that explicitly support quadratic constraints
• unsupported quadratic cases that should remain on the NLP path
• failure cases proving infeasible, error, or time-limit results are not silently converted into a fallback solve

Acceptance criteria

• The short-circuit path no longer duplicates the full constraint degree walk already done during utility-block setup.
• Continuous QP/QCP routing depends on explicit solver capability, not just degree classification.
• Existing quadratic_strategy behavior remains unchanged unless intentionally revised in the follow-up implementation.
• The current Fix no results returned when no discrete variables are present in MindtPy #3861 regression tests remain valid without broadening that PR scope.